High-input impedance tunable DDCCTA-based voltage-mode universal filter with grounded capacitors and resistors

Int. J. Electron. Commun. (AEÜ) 70 (2016) 491–499

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High-input impedance tunable DDCCTA-based voltage-mode universal filter with grounded capacitors and resistors Hua-Pin Chen, San-Fu Wang ∗ Dept of Electronic Engineering, Ming Chi University of Technology, Taiwan, ROC

a r t i c l e

i n f o

Article history: Received 28 August 2015 Accepted 22 January 2016 Keywords: Active filters Voltage-mode High-input impedance Universal biquad DDCCTA

a b s t r a c t A new high-input impedance tunable voltage-mode universal filter using two modified differential difference current conveyor transconductance amplifiers (DDCCTA), two grounded capacitors and three grounded resistors is presented. Because the input impedance of the proposed tunable voltage-mode universal filter is high, the input terminal can be directly connected to the next stage. The proposed circuit simultaneously provides universal voltage-mode lowpass, bandpass, highpass, bandreject and allpass filtering responses, without passive component-matching conditions or restrictions on input signals and enables independent control of the quality factor using single passive element. The use of only grounded capacitors and resistors makes the proposed circuit ideal for integrated circuit implementation. The active and passive sensitivities of the proposed circuit configuration are low. Simulation results verifying the theoretical analysis are also included. © 2016 Elsevier GmbH. All rights reserved.

1. Introduction There is growing interest in designing current-mode current conveyor-based active filters. This is attributed to their high signal bandwidths, greater linearity, larger dynamic range and lower power consumption [1]. Analog filters perform one of the most important functions of present day electronics system. These have been used in many applications in communications and control systems [2,3]. Developing filter functions that operate simultaneously in the same circuit topology increases their flexibility and versatility, and thus, their potential for practical application. Voltage-mode active filters using all grounded passive components have also been considered for use in integrated circuit (IC) implementation [4–6]. Meanwhile, high-input impedance voltage-mode active filters are of great interest because several cells of this kind can be directly connected in cascade to implement high-order filters [5–8]. Recently, the potential applications and advantages of realizing active filter transfer functions by using differential difference current conveyor transconductance amplifiers (DDCCTAs) have received considerable attention [9]. Subsequently, a highinput impedance DDCCTA-based voltage-mode multifunction biquadratic filter with a single input and three outputs, able to simultaneously realize voltage-mode highpass, bandpass and

∗ Corresponding author. E-mail address: sf [email protected] (S.-F. Wang). http://dx.doi.org/10.1016/j.aeue.2016.01.017 1434-8411/© 2016 Elsevier GmbH. All rights reserved.

lowpass filtering responses without passive component-matching conditions, was proposed in Tangsrirat et al. [10]. However, the bandreject and allpass filtering responses cannot be simultaneously realized from the same configuration. In 2012, Channumsin et al. [11] proposed a voltage-mode universal biquadratic filter with single input and five outputs using two DDCCTAs, two grounded capacitors and two grounded resistors. This circuit needs a component-matching condition to realize allpass filtering response. In 2013, an electronically tunable DDCCTA-based universal voltage-mode biquadratic filter with a single input and five outputs was proposed [12]. This circuit requires three DDCCTA active components. In the same year, an interesting DDCCTA-based universal biquadratic filter with single-input four-output was also proposed [13]. This circuit employs one DDCCTA, two grounded capacitors and two resistors. All the five standard biquadratic filter functions: lowpass, bandpass, highpass, bandreject and allpass, can be obtained from the circuit configuration. However, only four standard filter functions can be simultaneously obtained in this circuit realization. Two voltage-mode DDCCTA-based universal biquadratic filters were proposed [14,15]. However, these two configurations suffer from orthogonal controllability of the parameters resonance angular frequency and quality factor. Another voltage-mode DDCCTA-based universal biquadratic filter was also proposed in Chen et al. [16]. It joins one more important advantage of orthogonal controllability of the parameters resonance angular frequency and quality factor, but the resistors used are not all grounded. Theoretically, the voltage-mode biquadratic filter that permits the implementation of all basic filtering functions

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Table 1 Comparison of the proposed circuit with previously published DDCCTA-based voltage-mode multifunction/universal filters. Related works

No. of DDCCTAs

No. of passive elements

(i)

(ii)

(iii)

(iv)

(v)

(vi)

[10] [11] [12] [13] [14] [15] [16] Proposed

1 2 3 1 2 2 2 2

1R, 2C 2R, 2C 2C 2R, 2C 1R, 2C 2R, 2C 2R, 2C 3R, 2C

no yes yes no no yes yes yes

yes no yes no yes yes yes yes

no no no no no no yes yes

yes yes yes no yes yes yes yes

yes yes yes no yes yes no yes

yes yes yes yes yes yes no yes

lowpass, bandpass, highpass, bandreject and allpass responses without any component-matching conditions and enjoys the advantages of high-input impedance, all grounded passive elements, and orthogonal controllability of the resonance angular frequency and quality factor, is preferable in voltage-mode biquadratic filter design. In this paper, a new single input and six outputs highinput impedance tunable voltage-mode universal biquadratic filter using two modified DDCCTAs, two grounded capacitors and three grounded resistors is proposed. The proposed circuit enjoys the following advantages: (i) provides five biquadratic filter functions, that is, lowpass, bandpass, highpass, bandreject and allpass filters, simultaneously, from the same circuit configuration, (ii) does not require critical component-matching condition to realize all filter responses, (iii) offers independent adjustment of the quality factor by using one grounded resistor without disturbing the resonance angular frequency, (iv) has high-input impedances, which is desirable for cascading in voltage-mode operation, (v) employs all grounded passive elements, which is important in integrated circuit implementation point of view, and (vi) has low active and passive sensitivities. Comparison with recently reported DDCCTAbased biquad in [10–16] is given in Table 1. It can be seen that the proposed circuit does not require critical component-matching condition to realize the allpass filtering response and permits independent adjustment of quality factor. 2. Proposed circuit The schematic symbol is shown in Fig. 1. It has three highimpedance voltage inputs Y1 , Y2 , Y3 , one low-input current input X and four high-output current outputs Z1 +, Z2 +, O and O. The X terminal voltage follows the summation of the voltage Y3 and the voltage difference between terminals Y1 and Y2 . The current at terminal Z1 + follows the current at terminal X in positive magnitude. The Z2 + terminal is an extending output current terminal, which provides a copy of output current at the Z1 + terminal. The voltage VZ1 + on this terminal is transformed into current using the transconductance gm , which flows into output terminal O. The O terminal is an extending output current terminal, which provides a copy of output inverting current at the O terminal. This active element can be characterized by IY1 = IY2 = IY3 = 0, VX = VY1 –VY2 + VY3 ,

VY1 VY2 VY3

IY1 IY2 IY3

Z1+

Y1 Y2 DDCCTA Y3

Z2+ O O

X

IZ1+ VZ1+ I Z2+ VZ2+ IO VO IO VO

IX VX Fig. 1. Modified DDCCTA schematic symbol.

Fig. 2. Signal processing block diagram for realizing voltage-mode universal filter configuration.

Fig. 3. Proposed voltage-mode universal biquadratic filter.

IZ1+ = IX , IZ2+ = IX , IO = gm VZ1+ and I O = -gm VZ1+ , where gm is the transconductance parameter of the modified DDCCTA [12,13]. The gm -value is electrically controllable by input bias current, which leads electronic tunability to design circuit parameters. The block diagram representing the implementation of the single input and six outputs universal voltage-mode biquadratic filter is shown in Fig. 2. The configuration consists of two lossless integrators, three proportional gain block and three summers. The summer circuit of the universal voltage-mode biquadratic filter can be implemented easily with the modified DDCCTA. From the diagram in Fig. 2, the implementation of the high-input impedance voltage-mode universal circuit is shown in Fig. 3. It employs two modified DDCCTAs, two grounded capacitors and three grounded resistors. The input of the proposed circuit is applied to the Y terminals of the modified DDCCTAs. Thus, the circuit has the advantage of high-input impedance. Routine circuit analysis of Fig. 3 yields the six output voltage transfer functions as follows: Vo1 sC2 = Vin D(s)

(1)

Vo2 gm1 =− Vin D(s)

(2)

Vo3 sC2 gm1 R2 = Vin D(s)

(3)

Vo4 s2 C1 C2 R1 = Vin D(s)

(4)

Vo5 s2 C1 C2 R3 + gm1 gm2 R3 = Vin D(s)

(5)

Vo6 −s2 C1 C2 R1 + sC2 gm1 R2 − gm1 = Vin D(s)

(6)

D(s) is given by D(s) = s2 C1 C2 R1 + sC2 gm1 R2 + gm1

(7)

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Table 2 The aspect ratios of the CMOS transistors in modified DDCCTA implementation.

Fig. 4. Non-ideal equivalent circuit model of the modified DDCCTA.

From Eqs. (1)–(7), it can be seen that a non-inverting bandpass filtering function is obtained from Vo1 , an inverting lowpass filtering function is obtained from Vo2 , a non-inverting bandpass filtering function is obtained from Vo3 , a non-inverting highpass filtering function is obtained from Vo4 , a non-inverting bandreject filtering function is obtained from Vo5 and an inverting allpass filtering function is obtained from Vo6 . Thus, the proposed circuit simultaneously realizes all five biquadratic filtering functions from the same circuit configuration without any component-matching conditions. Due to the input signal is connected directly to the high-input impedance input node of the modified DDCCTAs, the circuit enjoys the feature of high-input impedance. It is also found from their transfer functions that no design passive components matching condition is required for any response. From the denominator polynomial of the transfer functions given in Eq. (7), the resonance angular frequency (ωo ) and the quality factor (Q) of the filter are expressed as:

 ωo =

gm1 , R1 C1 C2

1 Q = R2



R1 C1 gm1 C2

Transistors

L(␮m)

W(␮m)

M1–M4 M5–M9 M10–M14 M15–M16 M17–M22 M23–M26

0.35 0.18 0.18 0.5 0.8 0.8

8.75 17.5 8.75 10 25 8

By taking into account the non-idealities of modified DDCCTA, the relationship of the terminal voltages and currents can be rewritten as VX = ˇ1 VY1 - ˇ2 VY2 + ˇ3 VY3 , IZ1+ = ˛IX , IZ2+ = IX , IO = gm VZ1+ and I-O = -gm VZ1+ , where ˇk = 1-εvk for k = 1, 2, 3, ˛ = 1-ε˛i ,  = 1εi and  = 1-εi . Here, εvk (|εvk | < <1), ε˛i (|ε˛i | < <1), εi (|εi | < <1) and εi (|εi | < <1) represent the voltage and current tracking errors of the modified DDCCTA, respectively. Reanalysis of the proposed circuit in Fig. 3 yields the denominator of the non-ideal voltage transfer functions as follows: D(s) = s2 C1 C2 R1 + ˛1 ˇ21 1 sC2 gm1 R2 + ˛1 ˇ31 1 gm1

where ˇki , ˛i , i and  i are the parameters ˇk , ˛,  and  of the i-th modified DDCCTA (i = 1, 2), respectively. The filter parameters for the non-ideal ωo and Q were obtained as:



ωo =

From Eq. (8), the parameter Q can be independently tuned by using one grounded resistor R2 without disturbing ωo . In other words, parameters ωo and Q are orthogonal adjustable through the grounded R1 and then the grounded R2 in that order. This is a desired property in biquad filters due to the offered design and tuning flexibility. Note that this feature is not offered by the universal biquad in Chen [15] since its parameters ωo and Q are interactive. For the fix-valued capacitors, the ωo can be adjusted arbitrarily without disturbing Q by simultaneously changing gm1 and R1 (= R2 ), and keeping the product gm1 R1 constant. Thus, the proposed circuit permits orthogonal tunability of the parameters ωo and Q.

˛1 ˇ31 1 gm1 , R1 C1 C2

1 Q = ˇ21 1 R2



ˇ31 1 R1 C1 ˛1 gm1 C2

(10)

The active and passive sensitivities of the proposed circuit were given as o = −S ωo = −S ωo = −S ωo = S˛ω1o = Sˇωo = Sω1o = Sgωm1 R C C 1

31

1

2

SˇQ

= SQ1 = SRQ = SCQ = −S˛ω1o = −SgQm1 = −SCωo =

SˇQ

= SQ1 = SRQ = −1

31

21

(8)

(9)

1

1

2

2

1 2

1 2

(11) (12) (13)

These results indicated that all the sensitivities were low and not larger than unity in absolute value. The proposed circuit thus exhibited low-sensitivity performance. 3. Influence of parasitic elements A study is next carried out on the effects of various parasitic of the modified DDCCTA used in the proposed circuit. A practical modified DDCCTA device can be modeled as ideal modified DDCCTA with finite parasitic resistances and capacitances. Fig. 4 shows the non-ideal modified DDCCTA model including its parasitic elements. The non-zero parasitic input impedances at terminal X of the modified DDCCTA is represented by RX . The parasitic resistance RZ1 and parasitic capacitance CZ1 appear between the high-impedance

Fig. 5. CMOS implementation of the modified DDCCTA.

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Fig. 6. Theoretical and simulated frequency responses of the proposed circuit (a) bandpass filter (BP: Vo1 ), (b) lowpass filter (LP: Vo2 ).

Fig. 7. Theoretical and simulated frequency responses of the proposed circuit (a) bandpass filter (BP: Vo3 ), (b) highpass filter (HP: Vo4 ).

Fig. 8. Theoretical and simulated frequency responses of the proposed circuit (a) bandreject filter (BR: Vo5 ), (b) allpass filter (AP: Vo6 ).

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Fig. 9. Gain response of bandpass (Vo3 ) filters when R2 is varied (Q = 1: blue; Q = 2: red; Q = 5: green; Q = 10: pink; and Q = 20: purple).

Fig. 10. Demonstration of the maximum operating frequency range of bandpass (Vo 3 ) filters (fo = 16.218: blue; fo = 21.627: red; fo = 32.234: green; fo = 43.25: pink; and fo = 65.013: purple).

Z1 + terminal of the modified DDCCTA and grounded. The parasitic resistance RZ2 and parasitic capacitance CZ2 appear between the high-impedance Z2 + terminal of the modified DDCCTA and grounded. The parasitic resistance RO and parasitic capacitance CO appear between the high-impedance O terminal of the modified DDCCTA and grounded. The parasitic resistance R-O and parasitic capacitance C-O appear between the high-impedance O terminal of the modified DDCCTA and grounded. Because the X terminal of the modified DDCCTA1 in the proposed circuit of Fig. 3 is directly connected to an external resistor, the effect of parasitic resistance RX can easily be absorbed as a part of the main resistance. It is

further noted that the proposed circuit employs external capacitors C1 and C2 parallel connecting at the terminals Z1 + and O of the DDCCTA1, respectively. As a result, the effects of the parasitic capacitances CZ1 , CY3 and C-O can be absorbed, due to the fact that C1 » CZ1 and C2 » C-O , CY3 . Although the parasitic capacitances C-O and CY3 can be absorbed into the external capacitor C2 as it appears in shunt with it, the presence of parasitic resistances at terminals O and Y3 would change the type of the impedance which should be of a purely capacitive character. Hence, to minimize the effects of DDCCTA parasitic impedance, the values of the external capacitor used should be restricted to

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1 << RZ1 sC1

(14)

1 << (R−O //RY 3 ) s(C2 + C−O + CY 3 )

(15)

4. Simulation results To verify the theoretical study, H-Spice simulations were carried out to demonstrate the feasibility of the proposed circuit. The CMOS implementation of the modified DDCCTA is shown in Fig. 5 [12,13]. The dimensions of MOS transistors used in implementation of the modified DDCCTA are given in Table 2. The supply voltages were VDD = -VSS = 0.9 V, and the biasing voltage was VBB = 0.5 V. Figs. 6–8 show the simulated gain and phase responses for the bandpass (Vo1 ), lowpass (Vo2 ), bandpass (Vo3 ), highpass (Vo4 ), bandreject (Vo5 ) and allpass (Vo6 ) filters, respectively. The component values of Figs. 6–8 are chosen as gm = 200 ␮A/V (IB = 96.5 ␮A), R1 = R2 = R3 = 5 k, C1 = 3 pF and C2 = 6 pF, which is designed to obtain voltage-mode filter with a pole frequency fo = 7.5 MHz and the quality factor of Q = 0.707. By keeping the values of gm1 = gm2 = 100 ␮A/V, R1 = R3 = 10 k, C1 = C2 = 15.9 pF, fo = 1 MHz and varying only resistor of R2 with different values of 10, 5, 2, 1, 0.5 k results in bandpass responses at the Vo3 output terminal have the different Q values of 1, 2, 5, 10, 20, respectively. Thus, we obtain different Qs for the bandpass responses as shown in Fig. 9. It is important to note that the parameter Q can be adjusted by changing the resistor R2 without disturbing the center

frequency fo . To display the maximum operating frequency range of the proposed circuit, the simulated frequency responses of the bandpass (Vo3 ) filter at various operating center frequencies are shown in Fig. 10. As shown in the plots, the magnitude of the filter changed from 0.366 to 0.403 dB, in operation centre frequencies between 15.915 and 63.662 MHz. Table 3 shows the component values and corresponding ideal and simulated center frequencies. Note that simulation results demonstrated in Figs. 6–10 agree quite well with the theoretical ones as expected. Nonetheless, the difference between the theoretical and simulated responses mainly stems from the parasitic impedance effects and non-ideal gains of the modified DDCCTAs. The total power consumption is found to be 1.62 mW. The noise behavior of the filter was simulated using the INOISE and ONOISE statements of the frequency responses of bandpass (Vo3 ) response. Fig. 11 shows the simulated input and output noise amplitude responses for bandpass (Vo3 ) filters with INOISE and ONOISE, with gm1 = gm2 = 200 ␮A/V, R1 = R2 = R3 = 5 k, C1 = 3 pF and C2 = 6 pF. The total equivalent input and output noise √ voltages were 61.168 and 0.669 mV⁄ Hz, respectively. The output noise was extremely small and did not affect the output signal. To test the input dynamic range of Fig. 3, the simulation has been repeated for a sinusoidal input signal at fo = 7.5 MHz. Fig. 12a shows that the input dynamic range for the bandpass response at Vo3 output terminal with gm = 200 ␮A/V, R1 = R2 = R3 = 5 k, C1 = 3 pF and C2 = 6 pF, which extends up to amplitude of 0.5 V (peak to peak) without signification distortion. In Fig. 12a, the percent total harmonic distortion was 2.85%. The dependence of the output

Table 3 Component values for obtaining specified fo . Transconductance gm1 = gm2 , ␮A/V

Bias current IB1 = IB2 , ␮A

Resistance R1 = R2 = R3 , k

Capacitance C1 = C2 , pF

Calculated value of fo , MHz

Simulated value of fo , MHz

Frequency error, %

200 133.333 100 66.666 50

96.5 42.902 24.135 10.726 6.035

5 7.5 10 15 20

0.5 0.5 0.5 0.5 0.5

63.662 42.441 31.831 21.221 15.915

65.013 43.251 32.234 21.627 16.218

2.122 1.909 1.266 1.913 1.904

Fig. 11. Equivalent input (blue line) and output (red line) noise of bandpass (Vo3 ) filter against frequency.

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Fig. 12. Time-domain results of bandpass (Vo3 ) response (a) input (blue line) and output (red line) waveforms, (b) total harmonic distortion (THD) analysis results.

Fig. 13. Monte-Carlo 200 runs simulation analysis results for the bandpass (Vo3 ) frequency responses (a) Monte-Carlo analysis, (b) Monte-Carlo distribution.

harmonic distortion of the bandpass response at Vo3 on input voltage amplitude is illustrated in Fig. 12b. From Fig. 12b, we can see that the harmonic distortion rapidly increases if the input signal is increased beyond 0.25 V (peak) for the chosen modified DDCCTA implementation. To collect statistical data regarding mismatch and the variation effect, Monte-Carlo simulations were conducted. The device mismatch was modeled as a set of randomly generated samples that represented the probability distributions of the device parameters. The circuit was then repeatedly simulated with the random device samples, and performance data were collected. Fig. 13a shows the Monte-Carlo results for 200 simulation, regarding the bandpass frequency responses at Vo3 output terminal of Fig. 3 with gm = 200 ␮A/V, R1 = R2 = R3 = 5 k, C1 = 3 pF and C2 = 6 pF, in which all the passive components had a variation of 5% Gaussian deviation. According to the simulation, with a variation of centre frequency between 7.24 and 7.8 MHz, the fo -value of the bandpass filter was affected in the range of -3.47 to +4%. Fig. 13b compares the histogram of the center frequency obtained from the Monte-Carlo analysis. As the Monte-Carlo analysis results indicated, the proposed filter exhibited reasonable sensitivity performance.

Fig. 14. Example of implementation of the proposed circuit using commercially available OTAs.

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Fig. 15. The experimental evidence (a) bandpass (Vo1 : yellow line), lowpass (Vo2 : purple line) and high (Vo4 : cyan line) gain responses, (b) bandpass (Vo3 : purple line), bandreject (Vo5 : yellow line) and allpass (Vo6 : cyan line) gain responses.

Fig. 16. The input (channel 1) and output (channel 2) waveforms of bandpass output at Vo3 .

5. Measurement results The proposed filter configuration in Fig. 3 was experimentally tested. Because of the non-commercial IC of DDCCTA is available in the market, the proposed circuit realization based on the use of commercially MAX435s [17,18] is shown here in Fig. 14. The gm -value can be adjusted by an external resistor Rg (gm = 4/Rg ) of the MAX435 [17,18]. The DC power supply voltages ±5 V were used. The experimental measurements were performed with an Agilent N9000A CXA signal analyzer. Fig. 15a and b represents the frequency responses of the measurement results. The active and passive component values used in Fig. 15a and b were gm ≈ 4 mS, R2 = R3 = 250  and C1 = C2 = 1000 pF, and were designed to obtain center frequency of fo = 636.62 KHz. The resulted in bandpass response at the Vo1 output terminal with center frequency 611.33 KHz, with error of -3.97%. The resulted in bandreject response at the Vo5 output terminal with center frequency 633.82 KHz, with error of -0.44%. Time-domain responses were also investigated by applying a 2.8 V peak-to-peak input voltage sinusoidal at 636.6 KHz. Fig. 16 shows the input (channel 1) and output (channel 2) waveforms of the bandpass response at Vo3 output terminal. The obtained results show that the input dynamic of the filter extends up to amplitude of 2.8 V peak to peak without signification distortion. The phase error for the bandpass response is less than 3.8%. Therefore, the experimental results confirm the theoretical analyses. It should be mentioned that Fig. 15 is a measured result of a spectrum analyzer, which has input impedance of 50 , so that

the measured result of the gain has 5 dBm attenuations. Fig. 16 is the measured result of a scope with 10 M probe, which does not affect the experimental result of the circuit, so that the measured result of Fig. 14 circuit output is almost equal to the circuit input. On the other hand, in the measuring of the frequency domain, the 5 dBm attenuations are caused by the 50  input impedance of the spectrum analyzer. In the measuring of the time domain, the input signal and output signal are almost the same, because the scope and 10 M probe will not have amplitude attenuation of the circuit. Moreover, Fig. 16 shows the maximum input swing in time domain experimentation, when the output signal is not distorted. It must be mentioned that since the DDCCTA is not yet commercially available, it has been implemented by commercially available MAX435s due to the circuit’ verification support. However, in practice, an active element like DDCCTA would better be targeted for implementation of itself rather than being realized using four MAX435s. 6. Conclusions In this paper, a new single input and six outputs voltagemode universal biquadratic filter with high-input impedance is presented. The proposed circuit uses two modified DDCCTAs, two grounded capacitors and three grounded resistors. It also offers the following advantages: high-input impedance, simultaneous availability of lowpass, bandpass, highpass, bandreject and allpass filtering responses without component-matching conditions, the use of only grounded capacitors and resistors, low active and

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