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Ultra-low-noise TIA topology for MEMS gyroscope readout
Journal Pre-proofs Regular paper Ultra-Low-Noise TIA Topology for MEMS Gyroscope Readout Mahziar Serri, Saeed Saeedi PII: DOI: Reference:
S1434-8411(19)31718-2 https://doi.org/10.1016/j.aeue.2020.153145 AEUE 153145
To appear in:
International Journal of Electronics and Communications
Received Date: Revised Date: Accepted Date:
22 July 2019 21 February 2020 26 February 2020
Please cite this article as: M. Serri, S. Saeedi, Ultra-Low-Noise TIA Topology for MEMS Gyroscope Readout, International Journal of Electronics and Communications (2020), doi: https://doi.org/10.1016/j.aeue. 2020.153145
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Ultra-Low-Noise TIA Topology for MEMS Gyroscope Readout Mahziar Serri, Saeed Saeedi∗ Faculty of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran
Abstract This paper proposes a TIA topology that can be used in accelerometer and gyroscope systems. The proposed TIA topology considerably relaxes the trade-off among the transimpedance gain, bandwidth, and input referred current noise without increasing the power consumption. Furthermore, this paper presents a model for gyroscope microelectromechanical systems (MEMS) resonator that enables us, unlike prior works, to predict the resolution of the gyroscope system at the early stage of the design. In this model, the noise arising from driving loop blocks is compared with the noise of sense channel blocks. It has been illuminated that the noise of sense transimpedance amplifier (TIA) is the most influential in the resolution of the gyroscope system. To improve the resolution, the proposed TIA is employed in the sense channel of the gyroscope system. It enhances the resolution by about 57% compared with the conventional TIA employed in the sense channel. Measurement results of a discrete-element prototype also verify the performance improvement of the proposed TIA topology. Keywords: Microelectromechanical systems (MEMS), gyroscope, sense channel, transimpedance amplifier (TIA), input referred current noise, transimpedance gain. 1. Introduction MEMS-based inertial sensors can be found in many applications such as mobile devices, automobiles, oil exploration, seismic and inclinometers [1], [2], to name but a few. Among MEMS-based inertial sensors, MEMS gyroscope is used to measure the angular rate [3]. When the sensor undergoes a rotation around the z-axis the resultant Coriolis acceleration gives rise to the proof mass to vibrate along the y-axis. This induced rotation leads to the gap between the sense electrode and the proof mass to change proportional to the applied rate, resulting in changing in the capacitance. The resulting capacitance change can be detected by the readout circuit [4]. In the MEMS gyroscope with CMOS analog interface, not only does the low mechanical sensitivity make the detection so difficult but also the small sensing capacitance makes the design of the front end of the interface circuits a challenge [5]. The gyroscope consists of two parts: (1) drive oscillator (2) sense channel; in both of which, the capacitance variations need to be detected. As a result, there are two CMOS interface circuits that detect the displacement of capacitors. There are diverse front-end interface techniques for MEMS sensors [6]-[13]. The reference [14] compares the continuous time (CT) topologies with switched-capacitor (SC) topologies. Because of noise folding in SC topology, the CT circuit has better noise performance. With this in mind, transimpedance amplifiers (TIAs) are the most commonly used CT front-end interface circuits for the MEMS sensor [9]- [12], since it has high gain and low noise with low power consumption. However, existing TIA topologies still encounter with severe tradeoff among their bandwidth, noise, and trans-impedance gain. To relax the trade-off, ∗Corresponding
author. Email addresses: [email protected] (Mahziar Serri, MSc), [email protected] (Saeed Saeedi, PhD) ∗
Fig. 1. Schematic of scanning electron micrograph (SEM) of the Mode-Matched Tuning Fork Gyroscope (M2-TFG)\
a novel TIA topology is proposed in this paper. It has the lowest input referred current noise and highest transimpedance gain compared with the existing topologies at the same power consumption. Furthermore, the gyroscope sensors are susceptible to fabrication imperfections, external disturbances and ambient conditions. To overcome these problems, some developed control techniques have been implanted to the gyroscope system [15-19]. In addition to these problems, the readout circuit adds noise perturbations to the system. The noise sources in the circuit deteriorate the resolution of the system such that the applied angular velocity cannot be detected correctly. To address the noise effect of the readout circuit, in this paper, an elaborate model for the MEMS sensor gyroscope is presented. In contrast to the RLC model for the gyroscope sensor proposed in [10] and [20], this model can predict the performance of the gyroscope system at the early stage of the design. In this model, the effects of all noise sources are transferred to the output and resolution of the gyroscope system is calculated. It is also demonstrated that the TIA in the sense channel has a profound impact on noise performance. Therefore, the proposed low noise TIA, which is employed in the sense channel of the gyroscope system, improves the resolution performance. The remainder of this paper is organized as follows. Section 2 describes the structure of the gyroscope system. Section 3 introduces the proposed low-noise and high-gain TIA topology. Section 4 presents the proposed model for predicting its noise performance. Section 5 and 6 validate the proposed TIA topology, by simulation results of a TIA circuit implemented a 0.18μm CMOS technology and measurement results of a discrete TIA prototype, respectively. These sections are followed by the conclusion in section 7. 2. Structure of the Gyroscope System Fig. 1 shows the schematic of scanning electron micrograph (SEM) of the Mode-Matched Tuning Fork Gyroscope (M2-TFG). The twin proof-masses are centrally anchored and driven into resonant oscillation in opposite directions along x-axis applying voltage to feedback drive electrodes (drive mode). The drive electrode
produces a current signal which is converted to voltage by the interface circuit and can be applied back to the feedback drive electrode. When the sensor subjects to rotation about z-axis, Coriolis induced acceleration excites the proof-masses into resonance along the y-axis; the magnitude of applied rotation modulates the y-axis displacement amplitude. The resulting signal can be sensed from the sense electrode. Fig. 2 shows block diagram of the analog interface [12], [21]. The analog interface consists of two subsystems. The first one is the drive loop circuit which makes the reference vibrations along the x-axis. The second subsystem is the sense channel which converts the current of the sense electrode, Isense, to voltage by the TIAsense and demodulates the resulting signal. The readout circuit for the drive loop is divided into two parts: (i) the drive loop oscillator, including the front-end TIA, TIAdrive, and the feedback variable gain amplifier (VGA),
Fig. 2. The simplified MEMS gyroscope architecture [12] and [21]
which drives the MEMS resonator, and (ii) the automatic amplitude control (AAC) block to stabilize the oscillation amplitude. In the oscillator loop, the TIAdrive converts the Idrive to a voltage signal, VD in Fig.2. Transimpedance and bandwidth of this circuit should be large enough to satisfy the Barkhausen’s gain and phase Criteria and sustain the oscillation. The output of the TIAdrive is applied to the VGA and its amplitude information is also extracted by the amplitude detector in the AAC loop. Then, the error amplifier, the subtractor in Fig.2, subtracts the detected amplitude signal from the reference voltage, Vref, and amplifies the difference. The loop filter (LF) at the output of the error amplifier rejects the high frequency harmonics and generates a control voltage from the difference signal for controlling the gain of the VGA and stabilizing the oscillator amplitude. The chopper circuits in the AAC block is used for reducing the flicker noise. By employing the AAC loop, the output amplitude of the drive loop oscillator eventually approaches to a pre-defined value, which is set by Vref. 3. Proposed TIA Topology 3.1 Review of Pervious Works in TIA Design for MEMS Sensor Interface Fig. 3 shows various structures of TIAs in MEMS sensors. A single resistive feedback TIA structure was presented in [9] and is depicted in Fig. 3(a). CP which is created by the pad and bonding wires denotes input parasitic capacitor and is in pF range. 𝑅𝑓 is made of pseudo-resistor [22], [23] in order to achieve high gain as well as low input referred current noise. 𝐶𝑐 is used for compensation and strongly limits the bandwidth. Thus, the gain-bandwidth trade-off is a shortcoming in this work. The T-resistor network shown in Fig. 3(b) relieves the gain-bandwidth trade-off which is a drawback in Fig. 3(a) topology. In this topology, it is possible to extend the bandwidth since the same transimpedance with a smaller Rf can be achieved [10]. On the contrary, the power spectral density of input referred current noise is 1 + (𝑅2/𝑅1) times greater than the noise of single resistive feedback; therefore, noise is the primary disadvantage of this structure degrading the resolution of the whole system. The circuit schematic shown in Fig. 3(c), which is a capacitive-feedback current amplifier, amplifies the sensing current and converts it to the voltage through 𝑅𝑓. It uses capacitors in feedback path which are noiseless and in turn decrease the noise, but there is no dc feedback path for setting the bias point of the input. As a result, this topology needs to use the external DC bias circuit [11]. Although this topology yields higher gain and lower input referred current noise, the DC bias circuit increases input current noise, and
TABLE I KEY PERFORMANCE PARAMETERS OF PRIOR TIAs Gain
Bandwidth
Fig. 3(a)
𝑅𝑇𝑂𝑇 = 𝑅𝑓
Fig. 3(b)
𝑅𝑇𝑂𝑇 = 𝑅𝑓(1 +
Fig. 3(c)
𝑅𝑇𝑂𝑇 =
Fig. 3(d)
𝑅𝑇𝑂𝑇 =
Fig. 4 (proposed TIA)
𝑅𝑇𝑂𝑇 =
𝑅2 ) 𝑅1
𝑅𝑓𝐶2 𝐶1 𝑅𝑓𝐶2 𝐶1
𝑅2 𝑅𝑓𝐶2 (1 + ) 𝐶1 𝑅1
𝐵𝑊 =
1 𝑅𝑓𝐶𝑐
𝐵𝑊 =
1 𝑅𝑓𝐶𝑐
𝐵𝑊 = 𝐵𝑊 = [
𝐵𝑊 = [
𝑔𝑚1𝐴0𝐶1 𝐶2(𝐶1 + 𝐶𝑃) 1 1 ― ] 𝑅𝑏𝐶1 𝑅𝑓𝐶𝑐 1 1 ― ] 𝑅𝑏𝐶1 𝑅𝑓𝐶𝑐
Input current noise density 𝐼2𝑛 = 𝐼2𝑛 =
4𝑘𝐵𝑇
𝑅𝑓
-
𝑅𝑓
4𝑘𝐵𝑇
(1 +
𝑅2 ) 𝑅1
4𝑘𝐵𝑇 𝐶1 2 ( ) 𝑅𝑓 𝐶2 4𝑘𝐵𝑇 𝐶1 2 𝐼2𝑛 = ( ) 𝑅𝑓 𝐶2 𝐼2𝑛 =
𝐼2𝑛 =
𝐶1 2 ( ) 4𝑘𝐵𝑇 𝐶2 𝑅𝑓
Advantage
𝑅2 2 (1 + ) 𝑅1
Relaxing gainbandwidth trade-off
Disadvantage Gainbandwidth trade-off High input referred current noise
High gain and low noise
DC offset
Ultra-low noise
Gain, noisebandwidth trade-off
Relaxing trade-offs
-
Fig. 3. Prior TIA topologies: (a) single resistive feedback [9], (b) T-resistor network [10], (c) capacitive-feedback current amplifier [11] (d) conventional two-stage bandpass TIA [12]
also DC offset is an important issue. The topology shown in Fig. 3(d) is a band pass TIA which consists of two stages [12]. The first stage is an integrator and the second stage is a differentiator. This topology reduces the trade-off between noise and gain of the TIA, but there is scanty degree of freedom to achieve high bandwidth simultaneously. The TIAs' key performance parameters are summarized in Table I in which, only the noise arising from 𝑅𝑓 is considered for simplicity.
Fig. 4. The Proposed TIA topology
3.2 Proposed TIA Fig. 4 shows the schematic of the proposed TIA. This topology is a combination of T-network resistor and twostage topology. It has the benefits of two-stage topology which relaxes the trade-off among transimpedance and input referred current noise. In addition, according to the Fig. 3(b), by using T-resistor network, the trade-off between gain and bandwidth relaxes more and the degree of the freedom in the proposed TIA increases. The main novelty of this work is that, unlike the T-network topology which increases the power spectral density of input current noise compared to single resistive feedback, the T-network resistor in the proposed TIA leads to the improvement of the noise performance. The claim will be proved by theoretical equations and simulation results in this paper. This work is suitable for MEMS resonator accelerometer and gyroscope especially for the sense TIA. This topology includes two stages. The first one is the T-network integrator and the second one is differentiator. VCM is chosen equal to the value of common mode feedback's (CMFB) output of the first OTA (OTA1) in order to set the OTA1 input dc bias point. The proposed TIA has some advantages in comparison to prior TIAs and also the conventional two-stage topology. First, the highest transimpedance gain can be achieved among all other topologies mentioned in Table I. Second, the tradeoff between bandwidth and transimpedance is more relaxed in this topology compared to the others such that the dominant current noise from 𝑅𝑓 can be more attenuated. Third, the first stage, which acts as an integrator, attenuates the noises from both OTAs and this is an advantage compared to Fig. 3 (a), (b), and (c). Finally, 𝑅𝑏, 𝑅1, and 𝑅2 in the first stage and 𝑅𝑓 in the second stage provide the dc feedback path for the two OTAs and the second stage input is AC coupled. Therefore, the DC offset is not an issue anymore in contrast to Fig. 3 (c). 3.3 Frequency Response and Stability The frequency response of two stages of transimpedance gain at all frequencies can be computed as V OUT (s ) R 2 R b R f C 2s R 2 R f C 2s I SIG (s ) ( R f C c s 1) R 1 ( R b C 1s 1)( R f C c s 1)
(1)
R f C 2Rb s . ( R b C 1s 1)( R f C c s 1)
where the two OTAs are assumed ideal. Since this topology consists of an integrator and a differentiator, it has
band-pass frequency response. Low cutoff frequency ωL and high cut off frequency ωH and the simplified transimpedance gain at mid-band can be expressed as 1 , (R C ) b 1 1 , H ( R Cc ) f
RTOT (
L
R 2R f C 2 R f C 2 R C R ) f 2 ( 2 1). R1C 1 C1 C 1 R1
(2) (3) (4)
As we expected, the gain-bandwidth trade-off is relaxed more. For high bandwidth, the 𝑅𝑏 and 𝐶𝑐 can be set independent from transimpedance gain, and for high transimpedance gain, R1, R2, and C2 can be set independent from bandwidth. Transimpedance gain is improved by the value of (𝐶2/𝐶1) and R2/R1 ratios without the need for increasing 𝑅𝑓 which limits the bandwidth according to (3). In design of this TIA, the proper value of 𝑅𝑏 and 𝐶1 can guarantee that the 𝜔𝐿 becomes below the band of interest. The selection of 𝑅𝑓 and 𝐶𝑐 should be carried out such that the 𝜔𝐻 becomes much higher than the band of interest so that a well-behaved phase response is achieved. To consider the effect of OTA1 non-idealities on the frequency response, it is assumed that the OTA1 has one pole and finite transcunductance. The transimpedance function of the first stage at the mid-band, with the assumption of large value of 𝑅𝑏, can be computed as R 2 .RO 1.G m 1 R1.RO 1.G m 1 (5) ] H (s ) [ 1
(C O 1.R 2 C 1.R1 C O 1.R1 C 1.R 2 C 1.R1.RO 1.G m 1 C O 1.RO 1 RO 1.C 1 ).s
where 𝐺𝑚1 is the total transconductance of OTA1. 𝑅𝑂1 and 𝐶𝑂1 are the equivalent output resistor and the output capacitor of the OTA1, respectively. To attain (4) from (5), 𝐶1.𝑅𝑂1.𝑅1.𝐺𝑚1 should be bigger than the other terms in dominator. This result will be used in the design guide of the proposed TIA. To analyze stability of the proposed TIA the loop gain of the first stage can be computed as LG (s )
(R bC 1s 1).G m 1.RO 1 R2 (R b [( 1)C P C 1 ]s 1).(RO 1.(C O 1 C 2 )s 1) R1
(6)
where 𝐺𝑚1𝑅𝑂1is the dc gain of OTA1. For stability issue, zero frequency needs to be lower than the second pole of the loop gain. The stability is satisfied with Rb
RO 1C O 1 C 2 RO 1 C1
(7)
3.4 Noise Performance of the TIA Assuming the single ended OTA, Fig. 5 depicts the all noise sources in proposed TIA. According to Fig. 5, the input referred current noise can be computed and simplified in the mid-band as
Fig. 5. All noise sources in proposed TIA I n2 I nf2
V
2 n2
1 + I nb2 +V n12 ω 2 (C 1 + C P ) 2 + C 2 2 R2 2 ( ) ( + 1) C1 R1 (R 2 C 1 ) 2 (R 2 C 1 ) 2 1 + R f2C 22ω 2 + I n12 + I n22 R R R C R f2 ( 2 ) 2 ( 2 + 1) 2 ( 2 + 1) 2 ( 2 + 1) 2 C1 R1 R1 R1
(8)
C ( 1 )2 C2 4k B T R f ( R 2 + 1) 2 R1
where 𝐼2𝑛𝑓, 𝐼2𝑛𝑏 , 𝐼2𝑛1 and 𝐼2𝑛2 denote the input-referred current noises of 𝑅𝑓, 𝑅𝑏, 𝑅1 and 𝑅2, respectively, 𝑉2𝑛1 and 𝑉2𝑛2 denote the input referred voltage noises of OTAs (𝐼2𝑛𝑓 = 4kBT/𝑅𝑓, 𝐼2𝑛𝑏 = 4kBT/𝑅𝑏, 𝐼2𝑛1 = 4kBT/𝑅1 and 𝐼2𝑛2 = 4kBT/ 𝑅2). This equation proves that the T-network resistor topology in proposed TIA not only does not degrade the noise performance but also improves it. In addition, According to (8), the proposed approach not only attenuates the noise of 𝑅𝑓, like the two-stage topology, by (𝐶2/𝐶1)2 but also attenuates it by ((𝑅2/𝑅1) + 1)2. It shows that the (𝑅2/𝑅1) ratio, unlike the Fig. 3(b), improves the noise performance. Fig. 6 shows the plot of input referred current noise spectrum. 𝜔𝑐1, 𝜔𝑐2 and 𝜔𝑐3 are the criteria points where 𝑉2𝑛1 , 𝑉2𝑛2 and 𝐼2𝑛1 become equal to 𝐼2𝑛𝑓, respectively. They should be higher than the resonance frequency (𝜔0) to attain low input referred current noise. From the above analysis, the following criteria can be derived as design guideline of the proposed topology R
C R 2 2 R ( 2 ) ( 2 1) b f C R 1 1
R 1 , R 2 R f (C 2 R 2 0 ) 2
(9) (10)
Fig. 6. The plot of input referred current noise
V
2 n1
4 k BT Rf CP R 1)( 2 1) 0 ]2 [C 2 ( R1 C1
V n22 <
4k B T R f R C 22 ω02 + 1 2 f
(11)
(12)
If the above criteria are satisfied, the 𝑅𝑓 noise becomes dominant and is attenuated such that the noise performance of the TIA is improved. 4. Model of the Gyroscope System 4.1 Model of the MEMS Sensing Element Fig. 7 depicts the MEMS sensor model, employed in this work, that consists of both drive and sense blocks of the gyroscope system. This model, unlike RLC model which is used [10] and [20], enables us to simulate and predict the performance of the gyroscope system and improve the design performance before experimental works. The sensor structure is maintained at a DC polarization voltage (VDC) to provide the bias for capacitive transduction. VAC is the signal voltage which is applied to the feedback drive electrode. This model is comprehensive and is considered all equations for CMOS-MEMS resonator based on [24]. To scrutinize Fig. 7, the equations which are utilized in this figure are derived as follows. According to the Fig. 7, the drive voltage feedback converts to the electrostatic force and the expressions are F
1 dC (V A C V DC ) 2 2 dx
(13)
Fig. 7. The complete model of the MEMS sensor gyroscope
F A C F (V
DC
V
AC
) F (V
DC
)
dC V dx
DC
V
AC
.
(14)
where F is the electrostatic force, dC/dx is the change in comb capacitance which is assumed to be constant, and FAC is the AC component of the electrostatic force. Then, the motion equation along x direction is approximately given by m
d 2x 0
dt
2
c
0
dx k x F . AC 0 dt
(15)
where m0 is the mass of the sensor, x is the displacement of the proof mass, c0 is the damping coefficient and k0 is the spring constant. The Laplace transfer function of (15) gives (16) X (s ) 1 (16) H d (s ) . 2 FAC (s )
m 0s c 0s k 0
The current signal at the drive electrode, which is produced by the capacitive displacement, can be shown as dQ dC dx dC (17) I driv e V DC V DC . dt
dt
dt dx
The Coriolis force is created when the circuit undergoes the rotation (Ωz). The equation of Coriolis force is given by [25] (18) Fcor 2 m A z Similarly, the equation of Isense in the sense channel is achieved like the (17) but in the y-axis. Hs (s) is the same as the Hd (s). ω1 is the resonance frequency of both of them. If the sense mode frequency is equal to the drive mode frequency (mode-matched gyroscope [26]), the signal can be amplified as much as possible and the mechanical sensitivity is maximized. In the sense path, vA is multiplied by the rotation (Ωz). Therefore, the current of sense channel is an amplitude modulated (AM) signal. The AM output consists of the rate signal modulated on the carrier wave at the resonance frequency of the drive loop and its amplitude is proportional to the rotate signal. Table II shows the specific parameters of the gyroscope in this design and they are employed in next sections to evaluate the mechanical noise of the system. Table II
Specific Parameters of Gyroscope
Parameter
Value
Unit
Maximum drive displacement (qdrive)
4.3
μm
Quality factor (Q)
12000
-
8.5
KHz
0.26
m ◦/s/√Hz
Sensor resonance frequency (f1) Theoretical sensor Brownian noise floor
Fig. 8. The simplified model for the sense channel of the MEMS gyroscope
4.2 Noise Model of the Readout Circuit There is a claim in [21] without any proof that resolution is limited by the white noise level in the system. The noise level is usually dominated by the input current noise of the sense front-end TIA, since the mechanical Brownian noise is negligible. On the other hand, the bias instability is restricted by the flicker noise level. In this part, the following analysis proves that the resolution is determined by white noise especially by the input referred current noise of the sense TIA. In order to analyze resolution of the gyroscope system, the simplified model for the sense channel of the MEMS gyroscope in Fig. 8 is employed. According to the Fig. 2 and Fig. 7, VD is in-phase with the signal VA. In Fig. 8, the noise of all blocks of drive loop is transferred to vA and VD. vA includes both amplitude noise and phase noise. GM and GTIA denote MEMS sensor gain and TIA gain, respectively. GM is dC dy GM H s (1 ) V DC (19) dy dt NTIA and NMEMS denote additive noise of the sense TIA and mechanical Brownian noise, respectively. Based on [21], if the quality factor is high, the electrical noise is dominant and determines the resolution. As table II shows, the quality factor of the MEMS sensor is high so electrical noise is more influential than mechanical noise on resolution of gyroscope. In [27], it is proved that a narrowband noise in the vicinity of 𝜔1 can be expressed in terms of its quadrature components. Therefore, NTIA, because of resonance at 𝜔1, can be considered to be narrowband and can be expressed as (20) N TIA (t ) N I ,TIA (t ) cos 1t N Q ,TIA (t ) sin 1t . where 𝑁𝐼,𝑇𝐼𝐴(𝑡) and 𝑁𝑄,𝑇𝐼𝐴(𝑡) are baseband noise components and have the same spectrum. The value of their power spectral density (PSD) are two times of the PSD of 𝑁𝑇𝐼𝐴(𝑡). If we assume that Ωz is (Ω𝑧 = 𝐴𝑅. cos (𝜔2(𝑡)))
,the value of sense TIA output voltage (VC ) is V C (t ) ( A C )[cos(( 2 1 )t n , A (t )) cos((1 2 )t n , A (t ))] N
I ,T IA
(t ) cos(1 )t
(21)
N Q ,T IA (t ) sin(1 )t
where 𝑎𝑛,𝐴(𝑡) and 𝜑𝑛,𝐴(𝑡) are the amplitude noise and the phase noise of drive loop at vA. 𝜔1 and 𝜔2 denote drive oscillation frequency and frequency of rotation signal, respectively. AC is the amplitude of signal at VC and is equal to AC
A R an , A (t )G A R A AG
(22)
2
where 𝐺 denotes ( ―2𝑚.𝐺𝑀.𝐺𝑇𝐼𝐴), and AA is the amplitude of vA. As a result, the output signal after LPF, considering noise of the drive loop and the additive noise of sense channel, is ( A D an ,D ) AC
[cos( 2 (t )).cos( n , A (t ) n , D (t )) 2 sin( 2 (t )) sin( n , A (t ) n , D (t )) cos( 2 (t ))
V out (t ) N
DEM
(23)
cos( n , A (t ) n , D (t )) sin( 2 (t )) sin( n , A (t ) n , D (t ))]
( A D an ,D ) N
I ,T IA
2
cos( n , D (t ))
( A D a n , D ) N Q ,T IA 2
sin( n , D (t ))
where n ,D (t ) and an , D are the phase and amplitude noise at VD, respectively, and AD is the amplitude of signal at VD. NDEM denotes the noise of the multiplier and the low pass filter in the demodulator block. Because of existing noise sources (𝜑𝑛,𝐴(𝑡) and n ,D (t ) ) in the arguments of sine and cosine, (23) can be simplified to ( A D an ,D ) A C
[cos( 2 (t )) sin( 2 (t )) 2 ( n , A (t ) n , D (t )) cos( 2 (t )) sin( 2 (t ))
V out (t ) N
DEM
( n , A (t ) n , D (t ))]
( A D an ,D ) N
I ,T IA
2
( A D a n , D ) N Q ,T IA 2
(24) ( n , D (t ))
In (24), multiplication of two noise sources can be neglected and it can be simplified to V out (t ) N
DEM
AD N
I ,T IA
(t )
2 A D A R A AG cos( 2 (t )) 2 A A a (t )G A A A R a n , D (t )G ( D R n ,A ) cos( 2 (t )) 2 2
(25)
We will show in section 5 that the second term is much greater than the others; therefore, the noise of sense TIA is the dominant noise and determines the resolution of gyroscope system. In conclusion, low noise and high gain TIA in the sense channel are necessary.
TABLE III Parameters of the Proposed TIA and the Required Noise Performance of the OTAs
R1
100kΩ
CP
1pF
R2
100kΩ
C1
100fF
Rb
1TΩ
C2
4.5pF
Rf
1MΩ
CC
200fF
𝑽𝟐𝒏𝟏
< 24 𝑛𝑉/√𝐻𝑧
𝑉2𝑛2
< 125 𝑛𝑉/√𝐻𝑧
Fig. 9. The two-stage OTA with common mode feedback (CMFB)
5. Validation of Proposed TIA Topology 5.1 Design Procedure of the TIA Fig. 9 shows the two-stage OTA with common mode feedback (CMFB) that is used in the TIA. Two poles of OTAs become far from each other by pole splitting technique (𝐶𝐶,𝑂𝑇𝐴). 𝑅𝑧 is also added to remove right half plane zero. Equation (8) demonstrates that 𝑉2𝑛1 and 𝑉2𝑛2 are high pass filtered in the mid-band, thus the noise requirements of these OTAs are relaxed. In addition, 𝑉2𝑛2 is also attenuated by ((𝑅2/𝑅1) + 1)2 when referred to input. Therefore, the second OTA can be designed with low power consumption. The parasitic capacitor 𝐶𝑃 amplifies 𝑉2𝑛1; thus, OTA1 needs to be designed with low input voltage noise. Then, this OTA has more power consumption than the other one to satisfy (11). According to the (11) and (12), the noise requirement of the OTAs can be computed with the assumption of 𝐶𝑃 = 3 pF. The proper value of 𝑅𝑏 is chosen according to (2) and (7) as well as (9). For satisfying these equations, a large value of 𝑅𝑏 is needed in the band of interest. The large 𝑅𝑏 gives rise to low input referred current noise as shown in (9). Moreover, it can lead to improvement of amplifier stability. As a result, 𝑅𝑏 is implemented by a pseudo resistor and set to 1 TΩ. The selection of 𝑅1and 𝑅2 depends on (4), (5), (9) and (10). Equation (5) indicates that 𝑅1 should be large enough in order to achieve a large value of transimpedance. In addition, based on (3) and (8), the 𝑅2/𝑅1 ratio increases the transimpedance gain and decreases the input noise level. On the other hand, according to (9), if the 𝑅2/𝑅1 ratio becomes very large, it results in an extremely large value of the 𝑅𝑏. Hence, in this design 𝑅1and 𝑅2 are set equal to 100 kΩ that satisfies all above conditions.
Fig. 10. Gilbert cell used for demodulation [10]
According to (4) and (8), large (𝐶2/𝐶1) ratio and 𝑅𝑓 increase the transimpedance gain and decrease the input referred current noise. According to (2) and (3), the selection of 𝐶1 and 𝐶𝑐 should guarantee that the 3- dB low cutoff frequency becomes much lower than the band of interest and high cutoff frequency becomes much higher than the band of interest. As the bandwidth of TIA is about 1.5 Hz to 800 kHz in this design, 𝐶1, 𝐶2, 𝐶𝑐 and 𝑅𝑓 are selected to be 0.1 pF, 4.5 pF, 0.2 pF and 1 MΩ, respectively, considering the chip area. Then, the transimpedance gain will be 90 MΩ. Table III summarizes the characteristics of the proposed TIA and the required performance of both OTAs.
5.2 Design of the Readout Circuit Components In order to verify performance of the proposed TIA topology based on the gyroscope noise model, the MEMS sensor, which is presented in Fig.7 based on the description in [24], is modeled by a Verilog-A code in Spectre. The readout circuit components of the MEMS gyroscope system shown in Fig. 2 has been also designed in a 0.18μm CMOS technology according to the circuit topologies employed in [12], [21]. The VGA topology is a differential common-source amplifier with resistive degeneration. The degeneration resistors are implemented by transistors operating in linear region. The value of the resistors, and hence the gain of the amplifier, are controlled by the signal from the subtractor, shown in Fig.2. The amplitude detector in the AAC circuit is implemented by an alternating voltage follower circuit which acts as a rectifier to extract the amplitude information. A low flicker noise voltage-to-current (V-I) converter is employed as the subtractor. The output current of the converter is applied to a type-II loop filter to generate the signal for controlling the gain of the VGA. In the AAC block, the chopper stabilization technique is implemented by a switching circuit to suppress the effect of flicker noise. The chopper frequency is set to 100 kHz [12], [21]. In the sense channel, the proposed TIA converts the sense current to voltage. The resulting signal is multiplied by the output of the TIA in the drive loop for demodulation. The multiplier is a Gilbert cell as shown in Fig.10 [10]. A capacitor at the multiplier output acts as a low pass filter (LPF) to suppress the high frequency component and generate the rate signal.
200
Singel T-Network Proposed
Gain (dB)
180 160 140 120 100 80 100
102
104
106
108
Frequency (Hz)
(a)
200 Two-Stage
Gain (dB)
180
Proposed
160 140 120 100 80 100
102
104
106
108
Frequency (Hz)
(b) Fig. 11. Frequency response of the TIA topologies, (a) Single resistive feedback, T-resistor network and the proposed topologies, (b) Conventional Two-stage and the proposed topologies
5.3 Simulation Results Fig. 11 shows frequency response of some TIA topologies in Fig.3 at same gain with ideal OTAs. It indicates that the proposed TIA has the largest bandwidth at the same gain. In addition, Fig. 12 shows that the proposed TIA has the best noise performance compared to other topologies at same gain, verifying the equations in Table I. Fig. 13 depicts frequency responses of two OTAs. The first OTA has 70dB gain and the second one has 63dB. As shown in Fig. 13 the unity-gain bandwidth of the OTAs are about 100MHz which is higher than the TIA bandwidth. Therefore, the OTAs can be assumed as one pole system. Fig. 14 (a) shows the open loop gain and phase frequency response of the first stage, and it shows that the phase margin is 81.2 degrees. As shown in Fig. 14 (b), the phase margin of the second stage is 71.6 degrees.
Output Voltage Noise (uV/√Hz)
2 Single T-Network Proposed
1.5 1 0.5 0 100
102
104
Frequency (Hz)
106
108
Output Voltage Noise (uV/√Hz)
(a) 0.25 Two-Stage Proposed
0.2 0.15 0.1 0.05 0 100
102
104
106
108
Frequency (Hz)
(b) Fig. 12. Noise of the TIA topologies, (a) Single resistive feedback, T-resistor network and the proposed topologies, (b) Conventional Two-stage and the proposed topologies
Fig. 13. Frequency response of the two OTAs
Fig. 14. Open loop gain and phase of (a) first stage (b) second stage
Fig. 15. The layout of the proposed TIA
Layout of the proposed TIA in the 0.18μm CMOS technology is shown in Fig. 15. The size of the layout is 145 μm × 190 μm. Fig. 16 shows the post layout simulation result of the transimpedance gain which is 88 MΩ at mid-band frequencies. The low cutoff frequency and high cutoff frequency are 1.5 Hz and 795 kHz, respectively. Fig. 17 depicts the post layout simulation result of the TIA output voltage noise. It is 273 nV/√Hz and 221 nV/√Hz at 21 kHz and 8.5 kHz, respectively. The input referred current noise is 3.1 fA/√Hz and 2.5 fA/√Hz at 21 kHz and 8.5 kHz, respectively. It is the lowest reported simulated input referred current noise for a TIA employed in the MEMS gyroscope system to the authors’ knowledge.
Fig. 16. Post layout simulation result of transimpedance gain of the proposed TIA
Fig. 17. Post layout simulation result of the TIA output voltage noise
Table IV summarizes the simulation performance of the proposed TIA and compares it with performance of some reported TIA topologies for the MEMS sensor systems. Among the simulation results of the noise performance, our work shows the lowest input referred current noise. TABLE IV Performance summary of the proposed TIA and comparison with Prior Works Reference
[28]
[29]
[10]
[11]
[12]
This work
Transimpedance gain(simulation)
-
6.3kΩ
-
85MΩ
45MΩ
88MΩ
Transimpedance gain(measurement)
316kΩ
5.6 kΩ
1.6MΩ
56MΩ
44.5MΩ
-
Bandwidth
60MHz
2.5GHz
230kHz
1.8MHz
1Hz-450kHz
1.5Hz-795kHz
-
10pA/√Hz
-
41fA/√Hz
4.5fA/√Hz
3.1fA/√Hz
2.5pA/√Hz
~10pA/√Hz
88fA/√Hz
65fA/√Hz
6.6fA/√Hz
-
Supply(V)
2.5
1.5
±1.5
1.8
1.5
1.5
Power
5.9mW
7.2mW
400µW
436 µW
583µW
561µW
Process
0.18µm
0.18µm
0.6µm
0.6 µm
0.35µm
0.18µm
Input current noise (simulation) Input current noise (measurement)
Fig. 18. The comparison between noise of the sense TIA and noise of all blocks of the drive loop at the output
Fig. 19. The contribution of noise of the Gilbert cell and LPF
Fig. 18 compares noise effect of the sense TIA and the drive loop components at the output of the gyroscope system (VOUT in Fig. 8). In this simulation, the input frequency (ω2) is 100 Hz. Although the noise of drive loop increases at low frequency, the noise of sense TIA is still dominant at the mechanical bandwidth and it mainly determines the resolution of the gyroscope system. The noise effect of the Gilbert multiplier and the LPF, in the demodulator block, at the output is illustrated in Fig.19. Compared with the contribution of the sense TIA, shown in Fig.18, the noise effect of the demodulator circuit is negligible. Fig.18 and Fig.19 illustrate that a low noise and high gain sense TIA is required for improving resolution of gyroscope. Fig. 20 shows the simulation result of the gyroscope system resolution by employing the proposed TIA and the conventional two-stage band pass TIA. Compared to the two-stage topology which is simulated in our work, the proposed TIA has 57% better resolution. In this work, the resolution, which is determined by electrical noise of the gyroscope readout circuit, is 0.002 ◦/s/√Hz and the sensitivity of the gyroscope system is 3 mV/◦/s.
Fig. 20. The gyroscope system resolution by employing the proposed TIA and the conventional two-stage TIA of Fig. 3(d)
Fig. 21. Photograph of the discrete prototype.
6. Discrete Implementation of the TIA for Proof of Concept To illustrate performance of the proposed TIA topology relative to the two-stage topology of Fig.3(d), both of the TIAs are realized on a PCB board by employing commercially available components. The photograph of the discrete prototype is shown in Fig.21. The employed op-amp for the discrete implementation is an LM324 IC, which consists of four independent operational amplifiers. The high cutoff frequency of the discrete TIA is reduced compared with the CMOS TIA to comply with the unity-gain bandwidth of the LM324 op-amp. The other parameters of the proposed TIA in the discrete prototype, shown in Table V, are selected according to the design procedure in section 3, which is still valid regardless of the discrete or integrated implementation.
TABLE V Parameters of the Proposed TIA in the discrete prototype
R1
10 kΩ
C1
1 pF
R2
20 kΩ
C2
2 pF
Rb
100 MΩ
CC
1 pF
Rf
1 MΩ
Fig.22 shows the measured frequency response of both TIAs at the same gain. As illustrated in this figure, 3-dB bandwidth of the proposed TIA is 155 kHz and is about 3 times higher than the 3-dB bandwidth of the twostage circuit at the same gain. The measured output voltage noise of the TIAs is depicted in Fig.23. According to this figure, the output noise density of the proposed TIA and the two-stage TIA at the mid-band is about 200 and 300 nV/√Hz, respectively. These measurement results of the discrete prototype provide proof of the concept and shows superiority of the proposed topology compared with the conventional two-stage topology. 140
Proposed Two-stage
135 130
Gain (dB )
125 120
BW=50 KHz
115
BW=155 KHz
110 105 100 95 90
3
10
4
10
Frequency (Hz)
5
10
6
10
Fig. 22. Measured frequency response of the proposed TIA and the two-stage TIA at the same gain.
7. Conclusion In this paper, the elaborate model for MEMS gyroscope system has been presented that contains both drive and sense blocks. The behavior model of the system, implemented in Spectre by Verilog-A code, allows analyzing of the circuit noise effect and predicting the system resolution before experimental works. The analysis indicates that the noise of the sense TIA has the most impact on the resolution of the gyroscope. Therefore, we have proposed the TIA topology that relaxes the trade-off among noise performance, gain and bandwidth. The analysis of the proposed TIA topology shows that it has the highest transimpedance gain and the lowest input referred current noise compared with conventional TIA topologies employed in MEMS readout circuits. The simulation result of the gyroscope system indicates that employing the proposed TIA in the sense channel enhances the system resolution by about 57 % compared with employing the conventional two-stage TIA. The measurement results of the discrete prototype, realizing the proposed TIA and the two-stage TIA also demonstrate that the proposed TIA has higher 3-dB bandwidth and lower output noise density at the same gain.
-4
Output Voltage Noise (V/ Hz)
10
-5
10
200 nV/ Hz
-6
10
-7
10
-8
10 3 10
4
5
10
Frequency (Hz)
10
(a) -4
Output Voltage Noise (V/ Hz)
10
-5
10
300 nV/ Hz -6
10
-7
10
-8
10 3 10
4
10
Frequency (Hz)
5
10
(b) Fig. 23. Measured output voltage noise of, (a) the proposed TIA, and (b) the two-stage TIA, at the same gain.
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S1434-8411(19)31718-2 https://doi.org/10.1016/j.aeue.2020.153145 AEUE 153145
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International Journal of Electronics and Communications
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Please cite this article as: M. Serri, S. Saeedi, Ultra-Low-Noise TIA Topology for MEMS Gyroscope Readout, International Journal of Electronics and Communications (2020), doi: https://doi.org/10.1016/j.aeue. 2020.153145
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Ultra-Low-Noise TIA Topology for MEMS Gyroscope Readout Mahziar Serri, Saeed Saeedi∗ Faculty of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran
Abstract This paper proposes a TIA topology that can be used in accelerometer and gyroscope systems. The proposed TIA topology considerably relaxes the trade-off among the transimpedance gain, bandwidth, and input referred current noise without increasing the power consumption. Furthermore, this paper presents a model for gyroscope microelectromechanical systems (MEMS) resonator that enables us, unlike prior works, to predict the resolution of the gyroscope system at the early stage of the design. In this model, the noise arising from driving loop blocks is compared with the noise of sense channel blocks. It has been illuminated that the noise of sense transimpedance amplifier (TIA) is the most influential in the resolution of the gyroscope system. To improve the resolution, the proposed TIA is employed in the sense channel of the gyroscope system. It enhances the resolution by about 57% compared with the conventional TIA employed in the sense channel. Measurement results of a discrete-element prototype also verify the performance improvement of the proposed TIA topology. Keywords: Microelectromechanical systems (MEMS), gyroscope, sense channel, transimpedance amplifier (TIA), input referred current noise, transimpedance gain. 1. Introduction MEMS-based inertial sensors can be found in many applications such as mobile devices, automobiles, oil exploration, seismic and inclinometers [1], [2], to name but a few. Among MEMS-based inertial sensors, MEMS gyroscope is used to measure the angular rate [3]. When the sensor undergoes a rotation around the z-axis the resultant Coriolis acceleration gives rise to the proof mass to vibrate along the y-axis. This induced rotation leads to the gap between the sense electrode and the proof mass to change proportional to the applied rate, resulting in changing in the capacitance. The resulting capacitance change can be detected by the readout circuit [4]. In the MEMS gyroscope with CMOS analog interface, not only does the low mechanical sensitivity make the detection so difficult but also the small sensing capacitance makes the design of the front end of the interface circuits a challenge [5]. The gyroscope consists of two parts: (1) drive oscillator (2) sense channel; in both of which, the capacitance variations need to be detected. As a result, there are two CMOS interface circuits that detect the displacement of capacitors. There are diverse front-end interface techniques for MEMS sensors [6]-[13]. The reference [14] compares the continuous time (CT) topologies with switched-capacitor (SC) topologies. Because of noise folding in SC topology, the CT circuit has better noise performance. With this in mind, transimpedance amplifiers (TIAs) are the most commonly used CT front-end interface circuits for the MEMS sensor [9]- [12], since it has high gain and low noise with low power consumption. However, existing TIA topologies still encounter with severe tradeoff among their bandwidth, noise, and trans-impedance gain. To relax the trade-off, ∗Corresponding
author. Email addresses: [email protected] (Mahziar Serri, MSc), [email protected] (Saeed Saeedi, PhD) ∗
Fig. 1. Schematic of scanning electron micrograph (SEM) of the Mode-Matched Tuning Fork Gyroscope (M2-TFG)\
a novel TIA topology is proposed in this paper. It has the lowest input referred current noise and highest transimpedance gain compared with the existing topologies at the same power consumption. Furthermore, the gyroscope sensors are susceptible to fabrication imperfections, external disturbances and ambient conditions. To overcome these problems, some developed control techniques have been implanted to the gyroscope system [15-19]. In addition to these problems, the readout circuit adds noise perturbations to the system. The noise sources in the circuit deteriorate the resolution of the system such that the applied angular velocity cannot be detected correctly. To address the noise effect of the readout circuit, in this paper, an elaborate model for the MEMS sensor gyroscope is presented. In contrast to the RLC model for the gyroscope sensor proposed in [10] and [20], this model can predict the performance of the gyroscope system at the early stage of the design. In this model, the effects of all noise sources are transferred to the output and resolution of the gyroscope system is calculated. It is also demonstrated that the TIA in the sense channel has a profound impact on noise performance. Therefore, the proposed low noise TIA, which is employed in the sense channel of the gyroscope system, improves the resolution performance. The remainder of this paper is organized as follows. Section 2 describes the structure of the gyroscope system. Section 3 introduces the proposed low-noise and high-gain TIA topology. Section 4 presents the proposed model for predicting its noise performance. Section 5 and 6 validate the proposed TIA topology, by simulation results of a TIA circuit implemented a 0.18μm CMOS technology and measurement results of a discrete TIA prototype, respectively. These sections are followed by the conclusion in section 7. 2. Structure of the Gyroscope System Fig. 1 shows the schematic of scanning electron micrograph (SEM) of the Mode-Matched Tuning Fork Gyroscope (M2-TFG). The twin proof-masses are centrally anchored and driven into resonant oscillation in opposite directions along x-axis applying voltage to feedback drive electrodes (drive mode). The drive electrode
produces a current signal which is converted to voltage by the interface circuit and can be applied back to the feedback drive electrode. When the sensor subjects to rotation about z-axis, Coriolis induced acceleration excites the proof-masses into resonance along the y-axis; the magnitude of applied rotation modulates the y-axis displacement amplitude. The resulting signal can be sensed from the sense electrode. Fig. 2 shows block diagram of the analog interface [12], [21]. The analog interface consists of two subsystems. The first one is the drive loop circuit which makes the reference vibrations along the x-axis. The second subsystem is the sense channel which converts the current of the sense electrode, Isense, to voltage by the TIAsense and demodulates the resulting signal. The readout circuit for the drive loop is divided into two parts: (i) the drive loop oscillator, including the front-end TIA, TIAdrive, and the feedback variable gain amplifier (VGA),
Fig. 2. The simplified MEMS gyroscope architecture [12] and [21]
which drives the MEMS resonator, and (ii) the automatic amplitude control (AAC) block to stabilize the oscillation amplitude. In the oscillator loop, the TIAdrive converts the Idrive to a voltage signal, VD in Fig.2. Transimpedance and bandwidth of this circuit should be large enough to satisfy the Barkhausen’s gain and phase Criteria and sustain the oscillation. The output of the TIAdrive is applied to the VGA and its amplitude information is also extracted by the amplitude detector in the AAC loop. Then, the error amplifier, the subtractor in Fig.2, subtracts the detected amplitude signal from the reference voltage, Vref, and amplifies the difference. The loop filter (LF) at the output of the error amplifier rejects the high frequency harmonics and generates a control voltage from the difference signal for controlling the gain of the VGA and stabilizing the oscillator amplitude. The chopper circuits in the AAC block is used for reducing the flicker noise. By employing the AAC loop, the output amplitude of the drive loop oscillator eventually approaches to a pre-defined value, which is set by Vref. 3. Proposed TIA Topology 3.1 Review of Pervious Works in TIA Design for MEMS Sensor Interface Fig. 3 shows various structures of TIAs in MEMS sensors. A single resistive feedback TIA structure was presented in [9] and is depicted in Fig. 3(a). CP which is created by the pad and bonding wires denotes input parasitic capacitor and is in pF range. 𝑅𝑓 is made of pseudo-resistor [22], [23] in order to achieve high gain as well as low input referred current noise. 𝐶𝑐 is used for compensation and strongly limits the bandwidth. Thus, the gain-bandwidth trade-off is a shortcoming in this work. The T-resistor network shown in Fig. 3(b) relieves the gain-bandwidth trade-off which is a drawback in Fig. 3(a) topology. In this topology, it is possible to extend the bandwidth since the same transimpedance with a smaller Rf can be achieved [10]. On the contrary, the power spectral density of input referred current noise is 1 + (𝑅2/𝑅1) times greater than the noise of single resistive feedback; therefore, noise is the primary disadvantage of this structure degrading the resolution of the whole system. The circuit schematic shown in Fig. 3(c), which is a capacitive-feedback current amplifier, amplifies the sensing current and converts it to the voltage through 𝑅𝑓. It uses capacitors in feedback path which are noiseless and in turn decrease the noise, but there is no dc feedback path for setting the bias point of the input. As a result, this topology needs to use the external DC bias circuit [11]. Although this topology yields higher gain and lower input referred current noise, the DC bias circuit increases input current noise, and
TABLE I KEY PERFORMANCE PARAMETERS OF PRIOR TIAs Gain
Bandwidth
Fig. 3(a)
𝑅𝑇𝑂𝑇 = 𝑅𝑓
Fig. 3(b)
𝑅𝑇𝑂𝑇 = 𝑅𝑓(1 +
Fig. 3(c)
𝑅𝑇𝑂𝑇 =
Fig. 3(d)
𝑅𝑇𝑂𝑇 =
Fig. 4 (proposed TIA)
𝑅𝑇𝑂𝑇 =
𝑅2 ) 𝑅1
𝑅𝑓𝐶2 𝐶1 𝑅𝑓𝐶2 𝐶1
𝑅2 𝑅𝑓𝐶2 (1 + ) 𝐶1 𝑅1
𝐵𝑊 =
1 𝑅𝑓𝐶𝑐
𝐵𝑊 =
1 𝑅𝑓𝐶𝑐
𝐵𝑊 = 𝐵𝑊 = [
𝐵𝑊 = [
𝑔𝑚1𝐴0𝐶1 𝐶2(𝐶1 + 𝐶𝑃) 1 1 ― ] 𝑅𝑏𝐶1 𝑅𝑓𝐶𝑐 1 1 ― ] 𝑅𝑏𝐶1 𝑅𝑓𝐶𝑐
Input current noise density 𝐼2𝑛 = 𝐼2𝑛 =
4𝑘𝐵𝑇
𝑅𝑓
-
𝑅𝑓
4𝑘𝐵𝑇
(1 +
𝑅2 ) 𝑅1
4𝑘𝐵𝑇 𝐶1 2 ( ) 𝑅𝑓 𝐶2 4𝑘𝐵𝑇 𝐶1 2 𝐼2𝑛 = ( ) 𝑅𝑓 𝐶2 𝐼2𝑛 =
𝐼2𝑛 =
𝐶1 2 ( ) 4𝑘𝐵𝑇 𝐶2 𝑅𝑓
Advantage
𝑅2 2 (1 + ) 𝑅1
Relaxing gainbandwidth trade-off
Disadvantage Gainbandwidth trade-off High input referred current noise
High gain and low noise
DC offset
Ultra-low noise
Gain, noisebandwidth trade-off
Relaxing trade-offs
-
Fig. 3. Prior TIA topologies: (a) single resistive feedback [9], (b) T-resistor network [10], (c) capacitive-feedback current amplifier [11] (d) conventional two-stage bandpass TIA [12]
also DC offset is an important issue. The topology shown in Fig. 3(d) is a band pass TIA which consists of two stages [12]. The first stage is an integrator and the second stage is a differentiator. This topology reduces the trade-off between noise and gain of the TIA, but there is scanty degree of freedom to achieve high bandwidth simultaneously. The TIAs' key performance parameters are summarized in Table I in which, only the noise arising from 𝑅𝑓 is considered for simplicity.
Fig. 4. The Proposed TIA topology
3.2 Proposed TIA Fig. 4 shows the schematic of the proposed TIA. This topology is a combination of T-network resistor and twostage topology. It has the benefits of two-stage topology which relaxes the trade-off among transimpedance and input referred current noise. In addition, according to the Fig. 3(b), by using T-resistor network, the trade-off between gain and bandwidth relaxes more and the degree of the freedom in the proposed TIA increases. The main novelty of this work is that, unlike the T-network topology which increases the power spectral density of input current noise compared to single resistive feedback, the T-network resistor in the proposed TIA leads to the improvement of the noise performance. The claim will be proved by theoretical equations and simulation results in this paper. This work is suitable for MEMS resonator accelerometer and gyroscope especially for the sense TIA. This topology includes two stages. The first one is the T-network integrator and the second one is differentiator. VCM is chosen equal to the value of common mode feedback's (CMFB) output of the first OTA (OTA1) in order to set the OTA1 input dc bias point. The proposed TIA has some advantages in comparison to prior TIAs and also the conventional two-stage topology. First, the highest transimpedance gain can be achieved among all other topologies mentioned in Table I. Second, the tradeoff between bandwidth and transimpedance is more relaxed in this topology compared to the others such that the dominant current noise from 𝑅𝑓 can be more attenuated. Third, the first stage, which acts as an integrator, attenuates the noises from both OTAs and this is an advantage compared to Fig. 3 (a), (b), and (c). Finally, 𝑅𝑏, 𝑅1, and 𝑅2 in the first stage and 𝑅𝑓 in the second stage provide the dc feedback path for the two OTAs and the second stage input is AC coupled. Therefore, the DC offset is not an issue anymore in contrast to Fig. 3 (c). 3.3 Frequency Response and Stability The frequency response of two stages of transimpedance gain at all frequencies can be computed as V OUT (s ) R 2 R b R f C 2s R 2 R f C 2s I SIG (s ) ( R f C c s 1) R 1 ( R b C 1s 1)( R f C c s 1)
(1)
R f C 2Rb s . ( R b C 1s 1)( R f C c s 1)
where the two OTAs are assumed ideal. Since this topology consists of an integrator and a differentiator, it has
band-pass frequency response. Low cutoff frequency ωL and high cut off frequency ωH and the simplified transimpedance gain at mid-band can be expressed as 1 , (R C ) b 1 1 , H ( R Cc ) f
RTOT (
L
R 2R f C 2 R f C 2 R C R ) f 2 ( 2 1). R1C 1 C1 C 1 R1
(2) (3) (4)
As we expected, the gain-bandwidth trade-off is relaxed more. For high bandwidth, the 𝑅𝑏 and 𝐶𝑐 can be set independent from transimpedance gain, and for high transimpedance gain, R1, R2, and C2 can be set independent from bandwidth. Transimpedance gain is improved by the value of (𝐶2/𝐶1) and R2/R1 ratios without the need for increasing 𝑅𝑓 which limits the bandwidth according to (3). In design of this TIA, the proper value of 𝑅𝑏 and 𝐶1 can guarantee that the 𝜔𝐿 becomes below the band of interest. The selection of 𝑅𝑓 and 𝐶𝑐 should be carried out such that the 𝜔𝐻 becomes much higher than the band of interest so that a well-behaved phase response is achieved. To consider the effect of OTA1 non-idealities on the frequency response, it is assumed that the OTA1 has one pole and finite transcunductance. The transimpedance function of the first stage at the mid-band, with the assumption of large value of 𝑅𝑏, can be computed as R 2 .RO 1.G m 1 R1.RO 1.G m 1 (5) ] H (s ) [ 1
(C O 1.R 2 C 1.R1 C O 1.R1 C 1.R 2 C 1.R1.RO 1.G m 1 C O 1.RO 1 RO 1.C 1 ).s
where 𝐺𝑚1 is the total transconductance of OTA1. 𝑅𝑂1 and 𝐶𝑂1 are the equivalent output resistor and the output capacitor of the OTA1, respectively. To attain (4) from (5), 𝐶1.𝑅𝑂1.𝑅1.𝐺𝑚1 should be bigger than the other terms in dominator. This result will be used in the design guide of the proposed TIA. To analyze stability of the proposed TIA the loop gain of the first stage can be computed as LG (s )
(R bC 1s 1).G m 1.RO 1 R2 (R b [( 1)C P C 1 ]s 1).(RO 1.(C O 1 C 2 )s 1) R1
(6)
where 𝐺𝑚1𝑅𝑂1is the dc gain of OTA1. For stability issue, zero frequency needs to be lower than the second pole of the loop gain. The stability is satisfied with Rb
RO 1C O 1 C 2 RO 1 C1
(7)
3.4 Noise Performance of the TIA Assuming the single ended OTA, Fig. 5 depicts the all noise sources in proposed TIA. According to Fig. 5, the input referred current noise can be computed and simplified in the mid-band as
Fig. 5. All noise sources in proposed TIA I n2 I nf2
V
2 n2
1 + I nb2 +V n12 ω 2 (C 1 + C P ) 2 + C 2 2 R2 2 ( ) ( + 1) C1 R1 (R 2 C 1 ) 2 (R 2 C 1 ) 2 1 + R f2C 22ω 2 + I n12 + I n22 R R R C R f2 ( 2 ) 2 ( 2 + 1) 2 ( 2 + 1) 2 ( 2 + 1) 2 C1 R1 R1 R1
(8)
C ( 1 )2 C2 4k B T R f ( R 2 + 1) 2 R1
where 𝐼2𝑛𝑓, 𝐼2𝑛𝑏 , 𝐼2𝑛1 and 𝐼2𝑛2 denote the input-referred current noises of 𝑅𝑓, 𝑅𝑏, 𝑅1 and 𝑅2, respectively, 𝑉2𝑛1 and 𝑉2𝑛2 denote the input referred voltage noises of OTAs (𝐼2𝑛𝑓 = 4kBT/𝑅𝑓, 𝐼2𝑛𝑏 = 4kBT/𝑅𝑏, 𝐼2𝑛1 = 4kBT/𝑅1 and 𝐼2𝑛2 = 4kBT/ 𝑅2). This equation proves that the T-network resistor topology in proposed TIA not only does not degrade the noise performance but also improves it. In addition, According to (8), the proposed approach not only attenuates the noise of 𝑅𝑓, like the two-stage topology, by (𝐶2/𝐶1)2 but also attenuates it by ((𝑅2/𝑅1) + 1)2. It shows that the (𝑅2/𝑅1) ratio, unlike the Fig. 3(b), improves the noise performance. Fig. 6 shows the plot of input referred current noise spectrum. 𝜔𝑐1, 𝜔𝑐2 and 𝜔𝑐3 are the criteria points where 𝑉2𝑛1 , 𝑉2𝑛2 and 𝐼2𝑛1 become equal to 𝐼2𝑛𝑓, respectively. They should be higher than the resonance frequency (𝜔0) to attain low input referred current noise. From the above analysis, the following criteria can be derived as design guideline of the proposed topology R
C R 2 2 R ( 2 ) ( 2 1) b f C R 1 1
R 1 , R 2 R f (C 2 R 2 0 ) 2
(9) (10)
Fig. 6. The plot of input referred current noise
V
2 n1
4 k BT Rf CP R 1)( 2 1) 0 ]2 [C 2 ( R1 C1
V n22 <
4k B T R f R C 22 ω02 + 1 2 f
(11)
(12)
If the above criteria are satisfied, the 𝑅𝑓 noise becomes dominant and is attenuated such that the noise performance of the TIA is improved. 4. Model of the Gyroscope System 4.1 Model of the MEMS Sensing Element Fig. 7 depicts the MEMS sensor model, employed in this work, that consists of both drive and sense blocks of the gyroscope system. This model, unlike RLC model which is used [10] and [20], enables us to simulate and predict the performance of the gyroscope system and improve the design performance before experimental works. The sensor structure is maintained at a DC polarization voltage (VDC) to provide the bias for capacitive transduction. VAC is the signal voltage which is applied to the feedback drive electrode. This model is comprehensive and is considered all equations for CMOS-MEMS resonator based on [24]. To scrutinize Fig. 7, the equations which are utilized in this figure are derived as follows. According to the Fig. 7, the drive voltage feedback converts to the electrostatic force and the expressions are F
1 dC (V A C V DC ) 2 2 dx
(13)
Fig. 7. The complete model of the MEMS sensor gyroscope
F A C F (V
DC
V
AC
) F (V
DC
)
dC V dx
DC
V
AC
.
(14)
where F is the electrostatic force, dC/dx is the change in comb capacitance which is assumed to be constant, and FAC is the AC component of the electrostatic force. Then, the motion equation along x direction is approximately given by m
d 2x 0
dt
2
c
0
dx k x F . AC 0 dt
(15)
where m0 is the mass of the sensor, x is the displacement of the proof mass, c0 is the damping coefficient and k0 is the spring constant. The Laplace transfer function of (15) gives (16) X (s ) 1 (16) H d (s ) . 2 FAC (s )
m 0s c 0s k 0
The current signal at the drive electrode, which is produced by the capacitive displacement, can be shown as dQ dC dx dC (17) I driv e V DC V DC . dt
dt
dt dx
The Coriolis force is created when the circuit undergoes the rotation (Ωz). The equation of Coriolis force is given by [25] (18) Fcor 2 m A z Similarly, the equation of Isense in the sense channel is achieved like the (17) but in the y-axis. Hs (s) is the same as the Hd (s). ω1 is the resonance frequency of both of them. If the sense mode frequency is equal to the drive mode frequency (mode-matched gyroscope [26]), the signal can be amplified as much as possible and the mechanical sensitivity is maximized. In the sense path, vA is multiplied by the rotation (Ωz). Therefore, the current of sense channel is an amplitude modulated (AM) signal. The AM output consists of the rate signal modulated on the carrier wave at the resonance frequency of the drive loop and its amplitude is proportional to the rotate signal. Table II shows the specific parameters of the gyroscope in this design and they are employed in next sections to evaluate the mechanical noise of the system. Table II
Specific Parameters of Gyroscope
Parameter
Value
Unit
Maximum drive displacement (qdrive)
4.3
μm
Quality factor (Q)
12000
-
8.5
KHz
0.26
m ◦/s/√Hz
Sensor resonance frequency (f1) Theoretical sensor Brownian noise floor
Fig. 8. The simplified model for the sense channel of the MEMS gyroscope
4.2 Noise Model of the Readout Circuit There is a claim in [21] without any proof that resolution is limited by the white noise level in the system. The noise level is usually dominated by the input current noise of the sense front-end TIA, since the mechanical Brownian noise is negligible. On the other hand, the bias instability is restricted by the flicker noise level. In this part, the following analysis proves that the resolution is determined by white noise especially by the input referred current noise of the sense TIA. In order to analyze resolution of the gyroscope system, the simplified model for the sense channel of the MEMS gyroscope in Fig. 8 is employed. According to the Fig. 2 and Fig. 7, VD is in-phase with the signal VA. In Fig. 8, the noise of all blocks of drive loop is transferred to vA and VD. vA includes both amplitude noise and phase noise. GM and GTIA denote MEMS sensor gain and TIA gain, respectively. GM is dC dy GM H s (1 ) V DC (19) dy dt NTIA and NMEMS denote additive noise of the sense TIA and mechanical Brownian noise, respectively. Based on [21], if the quality factor is high, the electrical noise is dominant and determines the resolution. As table II shows, the quality factor of the MEMS sensor is high so electrical noise is more influential than mechanical noise on resolution of gyroscope. In [27], it is proved that a narrowband noise in the vicinity of 𝜔1 can be expressed in terms of its quadrature components. Therefore, NTIA, because of resonance at 𝜔1, can be considered to be narrowband and can be expressed as (20) N TIA (t ) N I ,TIA (t ) cos 1t N Q ,TIA (t ) sin 1t . where 𝑁𝐼,𝑇𝐼𝐴(𝑡) and 𝑁𝑄,𝑇𝐼𝐴(𝑡) are baseband noise components and have the same spectrum. The value of their power spectral density (PSD) are two times of the PSD of 𝑁𝑇𝐼𝐴(𝑡). If we assume that Ωz is (Ω𝑧 = 𝐴𝑅. cos (𝜔2(𝑡)))
,the value of sense TIA output voltage (VC ) is V C (t ) ( A C )[cos(( 2 1 )t n , A (t )) cos((1 2 )t n , A (t ))] N
I ,T IA
(t ) cos(1 )t
(21)
N Q ,T IA (t ) sin(1 )t
where 𝑎𝑛,𝐴(𝑡) and 𝜑𝑛,𝐴(𝑡) are the amplitude noise and the phase noise of drive loop at vA. 𝜔1 and 𝜔2 denote drive oscillation frequency and frequency of rotation signal, respectively. AC is the amplitude of signal at VC and is equal to AC
A R an , A (t )G A R A AG
(22)
2
where 𝐺 denotes ( ―2𝑚.𝐺𝑀.𝐺𝑇𝐼𝐴), and AA is the amplitude of vA. As a result, the output signal after LPF, considering noise of the drive loop and the additive noise of sense channel, is ( A D an ,D ) AC
[cos( 2 (t )).cos( n , A (t ) n , D (t )) 2 sin( 2 (t )) sin( n , A (t ) n , D (t )) cos( 2 (t ))
V out (t ) N
DEM
(23)
cos( n , A (t ) n , D (t )) sin( 2 (t )) sin( n , A (t ) n , D (t ))]
( A D an ,D ) N
I ,T IA
2
cos( n , D (t ))
( A D a n , D ) N Q ,T IA 2
sin( n , D (t ))
where n ,D (t ) and an , D are the phase and amplitude noise at VD, respectively, and AD is the amplitude of signal at VD. NDEM denotes the noise of the multiplier and the low pass filter in the demodulator block. Because of existing noise sources (𝜑𝑛,𝐴(𝑡) and n ,D (t ) ) in the arguments of sine and cosine, (23) can be simplified to ( A D an ,D ) A C
[cos( 2 (t )) sin( 2 (t )) 2 ( n , A (t ) n , D (t )) cos( 2 (t )) sin( 2 (t ))
V out (t ) N
DEM
( n , A (t ) n , D (t ))]
( A D an ,D ) N
I ,T IA
2
( A D a n , D ) N Q ,T IA 2
(24) ( n , D (t ))
In (24), multiplication of two noise sources can be neglected and it can be simplified to V out (t ) N
DEM
AD N
I ,T IA
(t )
2 A D A R A AG cos( 2 (t )) 2 A A a (t )G A A A R a n , D (t )G ( D R n ,A ) cos( 2 (t )) 2 2
(25)
We will show in section 5 that the second term is much greater than the others; therefore, the noise of sense TIA is the dominant noise and determines the resolution of gyroscope system. In conclusion, low noise and high gain TIA in the sense channel are necessary.
TABLE III Parameters of the Proposed TIA and the Required Noise Performance of the OTAs
R1
100kΩ
CP
1pF
R2
100kΩ
C1
100fF
Rb
1TΩ
C2
4.5pF
Rf
1MΩ
CC
200fF
𝑽𝟐𝒏𝟏
< 24 𝑛𝑉/√𝐻𝑧
𝑉2𝑛2
< 125 𝑛𝑉/√𝐻𝑧
Fig. 9. The two-stage OTA with common mode feedback (CMFB)
5. Validation of Proposed TIA Topology 5.1 Design Procedure of the TIA Fig. 9 shows the two-stage OTA with common mode feedback (CMFB) that is used in the TIA. Two poles of OTAs become far from each other by pole splitting technique (𝐶𝐶,𝑂𝑇𝐴). 𝑅𝑧 is also added to remove right half plane zero. Equation (8) demonstrates that 𝑉2𝑛1 and 𝑉2𝑛2 are high pass filtered in the mid-band, thus the noise requirements of these OTAs are relaxed. In addition, 𝑉2𝑛2 is also attenuated by ((𝑅2/𝑅1) + 1)2 when referred to input. Therefore, the second OTA can be designed with low power consumption. The parasitic capacitor 𝐶𝑃 amplifies 𝑉2𝑛1; thus, OTA1 needs to be designed with low input voltage noise. Then, this OTA has more power consumption than the other one to satisfy (11). According to the (11) and (12), the noise requirement of the OTAs can be computed with the assumption of 𝐶𝑃 = 3 pF. The proper value of 𝑅𝑏 is chosen according to (2) and (7) as well as (9). For satisfying these equations, a large value of 𝑅𝑏 is needed in the band of interest. The large 𝑅𝑏 gives rise to low input referred current noise as shown in (9). Moreover, it can lead to improvement of amplifier stability. As a result, 𝑅𝑏 is implemented by a pseudo resistor and set to 1 TΩ. The selection of 𝑅1and 𝑅2 depends on (4), (5), (9) and (10). Equation (5) indicates that 𝑅1 should be large enough in order to achieve a large value of transimpedance. In addition, based on (3) and (8), the 𝑅2/𝑅1 ratio increases the transimpedance gain and decreases the input noise level. On the other hand, according to (9), if the 𝑅2/𝑅1 ratio becomes very large, it results in an extremely large value of the 𝑅𝑏. Hence, in this design 𝑅1and 𝑅2 are set equal to 100 kΩ that satisfies all above conditions.
Fig. 10. Gilbert cell used for demodulation [10]
According to (4) and (8), large (𝐶2/𝐶1) ratio and 𝑅𝑓 increase the transimpedance gain and decrease the input referred current noise. According to (2) and (3), the selection of 𝐶1 and 𝐶𝑐 should guarantee that the 3- dB low cutoff frequency becomes much lower than the band of interest and high cutoff frequency becomes much higher than the band of interest. As the bandwidth of TIA is about 1.5 Hz to 800 kHz in this design, 𝐶1, 𝐶2, 𝐶𝑐 and 𝑅𝑓 are selected to be 0.1 pF, 4.5 pF, 0.2 pF and 1 MΩ, respectively, considering the chip area. Then, the transimpedance gain will be 90 MΩ. Table III summarizes the characteristics of the proposed TIA and the required performance of both OTAs.
5.2 Design of the Readout Circuit Components In order to verify performance of the proposed TIA topology based on the gyroscope noise model, the MEMS sensor, which is presented in Fig.7 based on the description in [24], is modeled by a Verilog-A code in Spectre. The readout circuit components of the MEMS gyroscope system shown in Fig. 2 has been also designed in a 0.18μm CMOS technology according to the circuit topologies employed in [12], [21]. The VGA topology is a differential common-source amplifier with resistive degeneration. The degeneration resistors are implemented by transistors operating in linear region. The value of the resistors, and hence the gain of the amplifier, are controlled by the signal from the subtractor, shown in Fig.2. The amplitude detector in the AAC circuit is implemented by an alternating voltage follower circuit which acts as a rectifier to extract the amplitude information. A low flicker noise voltage-to-current (V-I) converter is employed as the subtractor. The output current of the converter is applied to a type-II loop filter to generate the signal for controlling the gain of the VGA. In the AAC block, the chopper stabilization technique is implemented by a switching circuit to suppress the effect of flicker noise. The chopper frequency is set to 100 kHz [12], [21]. In the sense channel, the proposed TIA converts the sense current to voltage. The resulting signal is multiplied by the output of the TIA in the drive loop for demodulation. The multiplier is a Gilbert cell as shown in Fig.10 [10]. A capacitor at the multiplier output acts as a low pass filter (LPF) to suppress the high frequency component and generate the rate signal.
200
Singel T-Network Proposed
Gain (dB)
180 160 140 120 100 80 100
102
104
106
108
Frequency (Hz)
(a)
200 Two-Stage
Gain (dB)
180
Proposed
160 140 120 100 80 100
102
104
106
108
Frequency (Hz)
(b) Fig. 11. Frequency response of the TIA topologies, (a) Single resistive feedback, T-resistor network and the proposed topologies, (b) Conventional Two-stage and the proposed topologies
5.3 Simulation Results Fig. 11 shows frequency response of some TIA topologies in Fig.3 at same gain with ideal OTAs. It indicates that the proposed TIA has the largest bandwidth at the same gain. In addition, Fig. 12 shows that the proposed TIA has the best noise performance compared to other topologies at same gain, verifying the equations in Table I. Fig. 13 depicts frequency responses of two OTAs. The first OTA has 70dB gain and the second one has 63dB. As shown in Fig. 13 the unity-gain bandwidth of the OTAs are about 100MHz which is higher than the TIA bandwidth. Therefore, the OTAs can be assumed as one pole system. Fig. 14 (a) shows the open loop gain and phase frequency response of the first stage, and it shows that the phase margin is 81.2 degrees. As shown in Fig. 14 (b), the phase margin of the second stage is 71.6 degrees.
Output Voltage Noise (uV/√Hz)
2 Single T-Network Proposed
1.5 1 0.5 0 100
102
104
Frequency (Hz)
106
108
Output Voltage Noise (uV/√Hz)
(a) 0.25 Two-Stage Proposed
0.2 0.15 0.1 0.05 0 100
102
104
106
108
Frequency (Hz)
(b) Fig. 12. Noise of the TIA topologies, (a) Single resistive feedback, T-resistor network and the proposed topologies, (b) Conventional Two-stage and the proposed topologies
Fig. 13. Frequency response of the two OTAs
Fig. 14. Open loop gain and phase of (a) first stage (b) second stage
Fig. 15. The layout of the proposed TIA
Layout of the proposed TIA in the 0.18μm CMOS technology is shown in Fig. 15. The size of the layout is 145 μm × 190 μm. Fig. 16 shows the post layout simulation result of the transimpedance gain which is 88 MΩ at mid-band frequencies. The low cutoff frequency and high cutoff frequency are 1.5 Hz and 795 kHz, respectively. Fig. 17 depicts the post layout simulation result of the TIA output voltage noise. It is 273 nV/√Hz and 221 nV/√Hz at 21 kHz and 8.5 kHz, respectively. The input referred current noise is 3.1 fA/√Hz and 2.5 fA/√Hz at 21 kHz and 8.5 kHz, respectively. It is the lowest reported simulated input referred current noise for a TIA employed in the MEMS gyroscope system to the authors’ knowledge.
Fig. 16. Post layout simulation result of transimpedance gain of the proposed TIA
Fig. 17. Post layout simulation result of the TIA output voltage noise
Table IV summarizes the simulation performance of the proposed TIA and compares it with performance of some reported TIA topologies for the MEMS sensor systems. Among the simulation results of the noise performance, our work shows the lowest input referred current noise. TABLE IV Performance summary of the proposed TIA and comparison with Prior Works Reference
[28]
[29]
[10]
[11]
[12]
This work
Transimpedance gain(simulation)
-
6.3kΩ
-
85MΩ
45MΩ
88MΩ
Transimpedance gain(measurement)
316kΩ
5.6 kΩ
1.6MΩ
56MΩ
44.5MΩ
-
Bandwidth
60MHz
2.5GHz
230kHz
1.8MHz
1Hz-450kHz
1.5Hz-795kHz
-
10pA/√Hz
-
41fA/√Hz
4.5fA/√Hz
3.1fA/√Hz
2.5pA/√Hz
~10pA/√Hz
88fA/√Hz
65fA/√Hz
6.6fA/√Hz
-
Supply(V)
2.5
1.5
±1.5
1.8
1.5
1.5
Power
5.9mW
7.2mW
400µW
436 µW
583µW
561µW
Process
0.18µm
0.18µm
0.6µm
0.6 µm
0.35µm
0.18µm
Input current noise (simulation) Input current noise (measurement)
Fig. 18. The comparison between noise of the sense TIA and noise of all blocks of the drive loop at the output
Fig. 19. The contribution of noise of the Gilbert cell and LPF
Fig. 18 compares noise effect of the sense TIA and the drive loop components at the output of the gyroscope system (VOUT in Fig. 8). In this simulation, the input frequency (ω2) is 100 Hz. Although the noise of drive loop increases at low frequency, the noise of sense TIA is still dominant at the mechanical bandwidth and it mainly determines the resolution of the gyroscope system. The noise effect of the Gilbert multiplier and the LPF, in the demodulator block, at the output is illustrated in Fig.19. Compared with the contribution of the sense TIA, shown in Fig.18, the noise effect of the demodulator circuit is negligible. Fig.18 and Fig.19 illustrate that a low noise and high gain sense TIA is required for improving resolution of gyroscope. Fig. 20 shows the simulation result of the gyroscope system resolution by employing the proposed TIA and the conventional two-stage band pass TIA. Compared to the two-stage topology which is simulated in our work, the proposed TIA has 57% better resolution. In this work, the resolution, which is determined by electrical noise of the gyroscope readout circuit, is 0.002 ◦/s/√Hz and the sensitivity of the gyroscope system is 3 mV/◦/s.
Fig. 20. The gyroscope system resolution by employing the proposed TIA and the conventional two-stage TIA of Fig. 3(d)
Fig. 21. Photograph of the discrete prototype.
6. Discrete Implementation of the TIA for Proof of Concept To illustrate performance of the proposed TIA topology relative to the two-stage topology of Fig.3(d), both of the TIAs are realized on a PCB board by employing commercially available components. The photograph of the discrete prototype is shown in Fig.21. The employed op-amp for the discrete implementation is an LM324 IC, which consists of four independent operational amplifiers. The high cutoff frequency of the discrete TIA is reduced compared with the CMOS TIA to comply with the unity-gain bandwidth of the LM324 op-amp. The other parameters of the proposed TIA in the discrete prototype, shown in Table V, are selected according to the design procedure in section 3, which is still valid regardless of the discrete or integrated implementation.
TABLE V Parameters of the Proposed TIA in the discrete prototype
R1
10 kΩ
C1
1 pF
R2
20 kΩ
C2
2 pF
Rb
100 MΩ
CC
1 pF
Rf
1 MΩ
Fig.22 shows the measured frequency response of both TIAs at the same gain. As illustrated in this figure, 3-dB bandwidth of the proposed TIA is 155 kHz and is about 3 times higher than the 3-dB bandwidth of the twostage circuit at the same gain. The measured output voltage noise of the TIAs is depicted in Fig.23. According to this figure, the output noise density of the proposed TIA and the two-stage TIA at the mid-band is about 200 and 300 nV/√Hz, respectively. These measurement results of the discrete prototype provide proof of the concept and shows superiority of the proposed topology compared with the conventional two-stage topology. 140
Proposed Two-stage
135 130
Gain (dB )
125 120
BW=50 KHz
115
BW=155 KHz
110 105 100 95 90
3
10
4
10
Frequency (Hz)
5
10
6
10
Fig. 22. Measured frequency response of the proposed TIA and the two-stage TIA at the same gain.
7. Conclusion In this paper, the elaborate model for MEMS gyroscope system has been presented that contains both drive and sense blocks. The behavior model of the system, implemented in Spectre by Verilog-A code, allows analyzing of the circuit noise effect and predicting the system resolution before experimental works. The analysis indicates that the noise of the sense TIA has the most impact on the resolution of the gyroscope. Therefore, we have proposed the TIA topology that relaxes the trade-off among noise performance, gain and bandwidth. The analysis of the proposed TIA topology shows that it has the highest transimpedance gain and the lowest input referred current noise compared with conventional TIA topologies employed in MEMS readout circuits. The simulation result of the gyroscope system indicates that employing the proposed TIA in the sense channel enhances the system resolution by about 57 % compared with employing the conventional two-stage TIA. The measurement results of the discrete prototype, realizing the proposed TIA and the two-stage TIA also demonstrate that the proposed TIA has higher 3-dB bandwidth and lower output noise density at the same gain.
-4
Output Voltage Noise (V/ Hz)
10
-5
10
200 nV/ Hz
-6
10
-7
10
-8
10 3 10
4
5
10
Frequency (Hz)
10
(a) -4
Output Voltage Noise (V/ Hz)
10
-5
10
300 nV/ Hz -6
10
-7
10
-8
10 3 10
4
10
Frequency (Hz)
5
10
(b) Fig. 23. Measured output voltage noise of, (a) the proposed TIA, and (b) the two-stage TIA, at the same gain.
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