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Bonus Oscillators
10 Bonus Oscillators
Having spent countless days doing and redoing all of the demonstrations, recalculating all of the important parameters, performing and reperforming all of the simulations, examining the importance and the influence of each of the circuit’s parameters, it was then crucial to come up with a conclusion. Could we finally answer the fundamental question? Is there one and only one oscillator structure that outperforms all others? Part of the answer lies in the conclusions of Chapter 8, where we can fairly easily measure the supremacy of the series resonant Colpitts oscillator. As has been said over and over again, almost everything is based on the oscillating circuit’s quality factor. Leeson taught us the same thing in the form of his famous equation. Vackar, too, understood that in order to hide the harmful influence of the parasitic capacitances of the active element on the oscillating circuit, he had to insert a capacitive attenuator between the oscillating circuit and the amplifier. Another reflection is therefore necessary. It is useless and vain to want to separate Colpitts and Vackar. They are both right and their approach, consisting of favoring the oscillating circuit’s quality factor, is obviously the right one. Their approaches are not contradictory but complementary. A second thought comes next. Since Vackar’s way is proving to be wise, why not apply it to each side of the oscillating circuit, toward the source and the load? This amounts to placing a capacitive attenuator L on both sides of the oscillating circuit. Figure 10.1 represents these two oscillator topologies, which we decided to call Bora.
388
Amplifiers and Oscillators
Serial resonance
Parallel resonance
−G
C6
−G VE
C5
R
VE
L0 C0
C6
L0 C1
C3
C2
C4
VS
R1
C4
C2
C1
C5
R
C3
R1
VS
Figure 10.1. Topology of complementary oscillators, series or parallel resonance
In the diagram of Figure 10.1, the series or parallel resonant circuit is recognized, and then on either side of this circuit, we place two L-shaped capacitive attenuators. The computation having been carried out in the case of the Vackar oscillator, it is possible to directly apply the conclusions. The lower the values of capacitors C3 and C5 compared to C4 and C6, the better the efficiency of the L attenuators. In the case of the Vackar oscillator, the attenuation presented by the L attenuator must be compensated by the amplifier gain to satisfy the oscillation condition. In this final chapter, we therefore propose to examine the operation of these two oscillators only by the use of the simulator. The knowledge of the theoretical results of the Colpitts and Vackar oscillators is sufficient to realize the complete design of the oscillator without committing errors. The diagram in Figure 10.2 shows the first parallel resonance oscillator. Two successive transformations show that this oscillator is part of the series resonant Colpitts family. The first transformation is a star delta transposition that transforms PI attenuators into T attenuators. The second transformation groups capacitors C03 and C06. The set gives C0. We finally recognize the series resonant Colpitts oscillator framed by two capacitors. These two additional capacitors have an important role that is not limited to the suppression of the DC component. They intervene in phase noise, pulling and pushing.
Bonus Oscillators
−G VE
C5
R 1
C6
C05 C06
−G
L0
C3
C2 C1
C4
L0
C 03
R1
389
VS
C 04
R
C 01
C02
VE
R1
VS
2
C 05
−G
L0
C0
C04
R
C02
VE
C01
R1
VS
Figure 10.2. Successive transformation of the oscillator, parallel resonance
By placing a capacitive L-shaped elevator upstream of the resonant circuit, the attenuating effect of the capacitive divider placed downstream of the resonant circuit is annihilated. Without establishing the equations, or performing the calculation of the important oscillator parameters, we can realize that we will have all of the advantages and benefits envisaged by Vackar, without incurring the counterpart, which is a required increased gain. Since the oscillating circuit is placed between two symmetrical L-shaped circuits, it can be clearly seen that the oscillation frequency and oscillation condition will be identical to those which would be obtained without these two appendices upstream and downstream. We cannot say anything more without doing the calculation, as far as stability is concerned. 10.1. Parallel resonance oscillator The diagram of the Bora oscillator with parallel resonance is shown in Figure 10.3 along with the spectrum obtained in Transient simulation. This simulation is not necessary; its only role is to give information on the oscillation frequency.
390 Amplifiers and Oscillators
Figure 10.3. Transient simulation of the oscillator, parallel resonance
Bonus Oscillators
391
The design of this oscillator was limited to reproducing a Vackar oscillator to which was added an L capacitive divider. The most important and spectacular results are given by the Harmonic Balance simulation, the results of which are given in Figure 10.4.
Figure 10.4. Harmonic Balance simulation of the oscillator, parallel resonance
The oscillation frequency is 435.6 MHz. The spectrum in Figure 10.4 indicates that the power of the fundamental is approximately 0dBm and the second harmonic is rejected at 5.5 dB, which is not ideal. The results for phase noise are excellent, –136 dBc/Hz at 1 kHz of the carrier, then –155 dBc/Hz at 10 kHz and finally –167 dBc/Hz at 100 kHz. The circuit’s consumption is 4.3 mA under a supply voltage of 5 V, which leads us to an FOM of 235 dBF, which is quite respectable. We can then evaluate the oscillator’s pushing and pulling as has been done in all other cases. The results are shown in Figure 10.5; the pushing has a low value of 1.5 kHz/V. This value is at least 10 times lower than what is obtained in the best case. The pulling is also down by a factor of more than 10 compared to the best previous results, –0.7 kHz. The two capacitive attenuators placed on either side of the oscillating circuit perfectly played their role by considerably improving the phase noise, the FOM, the pushing and the pulling. The performance is compiled in Table 10.1. The results are comparable to those obtained with a SAW oscillator.
392
Amplifiers and Oscillators
Figure 10.5. Pushing and pulling simulation of the oscillator, parallel resonance
Frequency Pout MHz dBm 435
0
dBc/Hz Phase noise Pulling 1 kHz 10 kHz MHz 100 kHz 1 MHz -136 -155 -167
Pushing MHz/V
Harmonics dBc
1.5
5
-0.7
Tuning Power supply Sensitivity Voltage Current MHz/V (V) (mA) -
5
4.3
FOM dBF 235
Table 10.1. Summary table of oscillator performance, parallel resonance
This oscillator works perfectly when the supply voltage decreases to 3.3 V. The performances are preserved and the merit factor is always close to 235 dBF. To improve these performances, the two low-value capacitors C7 and C8, equal to 1pF in Figure 10.3, must be reduced, and this constitutes the major difficulty as these values are difficult to control. To facilitate the design of such an oscillator, it is sufficient to proceed in stages. The first stage consists of designing the basic oscillator, without the two capacitive L-shaped circuits. It is therefore a classic Colpitts oscillator. We can then simulate and record the oscillator’s performance. Finally, we add the two L-shaped capacitive circuits, chosen so that the ratios C7/C10 and C8/C9 are large, and the results are compared with those obtained previously. This design by stages proves that the design of such an oscillator is as simple as those found in all other cases. 10.2. Series resonant oscillator To design the series resonant oscillator, simply replace the coil with a coil in series with a capacitance. The lowest value is then given to the series capacitance, and then the value of the coil is calculated to obtain the desired frequency. This procedure maximizes the quality factor. The diagram of the Bora oscillator with series resonance is shown in Figure 10.6 along with the spectrum obtained in Transient simulation.
Bonus Oscillators
Figure 10.6. Transient simulation of the oscillator, series resonance
393
394
Amplifiers and Oscillators
The Transient simulation is not necessary, and, in any case, we must act with great care because the oscillator’s start-up time is quite long, in the order of a few milliseconds. If the simulation time is not long enough, the output level is measured during the start-up phase and the result does not make sense. There is nevertheless another piece of information which is quite reliable: the oscillation frequency, which is close to 473 MHz. HB shows that the oscillation frequency is 473.6 MHz. The spectrum in Figure 10.7 indicates that the power of the fundamental is approximately 0dBm and the second harmonic is rejected at 6.0 dB which, as in the previous case, is not ideal.
Figure 10.7. Harmonic Balance simulation of the oscillator, series resonance
The results for phase noise are excellent, –153 dBc/Hz at 1 kHz of the carrier, then –166 dBc/Hz at 10 kHz and finally –167 dBc/Hz at 100 kHz. The circuit’s consumption is 4.3mA under a supply voltage of 5 V, which leads us to an FOM of 253 dBF, which is perfect. It is still possible to gain some dB by optimizing the values of the circuit shown in Figure 10.6 but it seems impossible to cross the limit of 257 dBF, which is quite remarkable. We can then evaluate the pushing and pulling of the oscillator as has been done in all other cases. The results are shown in Figure 10.8; pushing and pulling have values that are at least 10 times lower than what was obtained in the previous case.
Bonus Oscillators
476.33662
m2
476.33660
m1 X= 4.500000 freq[::,1]=476.3365M
476.33658
395
476.33659m1 476.33658
m1 X= 45.00000 freq[::,1]=476.3366M
476.33657 476.33656
476.33656 476.33655 476.33654
m2 X= 5.500000 freq[::,1]=476.3366M
476.33652 476.33650m1
476.33654
m2 X= 55.00000 freq[::,1]=476.3365Mm2
476.33653 476.33652 476.33651
476.33648 4.5
4.6
4.7
4.8
4.9
5.0
5.1
5.2
5.3
5.4
45
5.5
46
47
48
49
50
51
52
53
54
55
X
X
Figure 10.8. Pushing and pulling simulation of the oscillator, series resonance
The pushing has a value of 0.11 kHz/V and the pulling, also down by a factor greater than 10 compared to the previous result, has a value of –0.07 kHz. The performances of this oscillator are grouped in Table 10.2. We are here in the presence of the best configuration that combines good performance with phase noise, pulling and pushing. Reconciling the ideas of Colpitts and Vackar is thus an excellent idea. Frequency Pout MHz dBm 476
0
dBc/Hz Phase noise Pulling MHz 1 kHz 10 kHz 100 kHz 1 MHz -153 -166 -167
-0.07
Pushing MHz/V
Harmonics dBc
0.11
6
Tuning Power supply Sensitivity Voltage Current MHz/V (V) (mA) -
5
4.3
FOM dBF 253
Table 10.2. Summary table of oscillator performance, series resonance
10.3. Differential oscillator, improvements It is questionable whether the solution of masking the drifts due to variations in parasitic capacitance for the introduction of a capacitive divider is applicable to other types of oscillators. We are particularly interested in the differential oscillator. During previous analyses, it was found that the differential oscillator had two major defects, a moderate phase noise and a very poor value of pushing. If the power is transmitted to the load via an auxiliary amplifier, the value of the pulling is satisfactory and this is the case of the oscillator shown in Figure 10.9. We therefore decided to repeat the diagram in Figure 10.9 and perform two tests, the first with a simple parallel resonant circuit connected between the two collectors and a second by interposing capacitive dividers.
396
Amplifiers and Oscillators
10.3.1. Differential oscillator, basic diagram The first tested oscillator corresponds to the diagram in Figure 10.9. The results of the first test are given in Figures 10.10 and 10.11. The output spectrum as well as the phase noise is given in Figure 10.10. The oscillation frequency is 625.2 MHz, the output level of the fundamental is –11.8 dBm, and the harmonics are, at best, rejected at 10 dBc. The phase noise at 1 kHz of the carrier is not exceptional and is equal to –90.7 dBc/Hz. Consumption is 5.4 mA, giving a merit factor of 192 dBF, which is quite ordinary.
Figure 10.9. Basic differential oscillator. For a color version of this figure, see www.iste.co.uk/dieuleveult/amplifiers.zip
Figure 10.10. Basic differential oscillator, spectrum and phase noise
Bonus Oscillators
397
Figure 10.11. Basic differential oscillator, pushing and pulling
With the phase noise curve shown in Figure 6.3, we have the value of the noise floor, equation [10.1], and the value of the frequency at which the phase noise joins the noise floor, equation [10.2]: −
=
− −
[10.1] = −174 +
=
−3− [10.2]
With the results shown in Figure 10.10, we have the noise floor which is –155 dBc/Hz and the frequency at which the phase noise joins the noise floor, 5 Mz. Knowing that the output power is –12 dBm, we can deduce a noise factor of 10 dB. Knowing that the oscillation frequency is 620 MHz, we deduce the quality factor Q = 62. These results show that it is likely that this oscillator can be improved by acting on the output power and on the noise factor. Figure 10.11 shows the result of pulling and pushing tests. An amplifier interposed between the oscillator and the output plays the role of isolation and provides an excellent pulling value, 1.35 kHz for a variation of 10 Ohms of the load. By contrast, the value of pushing is execrable and reaches 1.2 MHz/V and is similar to a control input of a VCO. By examining the schematic diagram of Figure 10.9, it can be seen that the two bases of the transistors constituting the oscillator are polarized by voltages of 3 V,
398
Amplifiers and Oscillators
which are assumed to be stabilized. In the pushing analysis, only the 5 V supply voltage is subject to variations. The influence of the parasitic base collector capacitances which, varying with the base collector voltage, act on the oscillation frequency is therefore measured. 10.3.2. Differential oscillator, Q increase Our goal, therefore, is to develop a circuit capable of masking the variations of the base collector capacitors. The idea is to transpose the previous structure and to insert capacitive dividers. These ideas are implemented in the diagram of Figure 10.12. Both capacitors C7 and C8 are of low value, 1pF, and capacitor C9 is of high value, 12pF. Two resistors R23 and R24 complement the device, as was the case in the improved Colpitts oscillator presented at the beginning of this chapter.
Figure 10.12. Differential oscillator with improved oscillating circuit. For a color version of this figure, see www.iste.co.uk/dieuleveult/amplifiers.zip
Here, the two additional capacitors constitute a current divider. The simulation results are given in Figure 10.13 for spectrum and phase noise and Figure 10.14 for pushing and pulling. The only difference between the diagrams in Figures 10.9 and 10.12 is the nature of the oscillating circuit connected between the two collectors of the oscillator. All other parameters are identical in terms of component values and operating point.
Bonus Oscillators
399
Figure 10.13. Basic differential oscillator, spectrum and phase noise
The spectrum shows that the output power is slightly diminished and goes to just under –12 dBm, a decrease of 0.4 dB. The rejection of harmonics is 8 dB at best; the result has deteriorated by approximately 2 dB. These two small disappointments are acceptable, compared to the performance on the phase noise which passes at –144 dBc/Hz at 1 kHz of the carrier and –154 dBc/Hz at 10 kHz of the carrier. The current drawn is unchanged, giving a remarkable merit factor of 246 dBF. The gain provided by the capacitive divider is considerable: 54 dB on the phase noise at 1 kHz of the carrier and 43 dB at 10 kHz of the carrier. The only criticism that can be made about this oscillator is the value of the phase noise floor of –155 dBc at 1 MHz of the carrier. This parameter can probably be improved. The values of pushing and pulling are given in Figure 10.14: 1.4 kHz/V for pushing and 2.9 kHz for pulling. The pushing has been improved by a factor of about 1000. This confirms the interest of the capacitive divider.
Figure 10.14. Differential oscillator with improved oscillating circuit, pushing and pulling
We can also calculate the apparent quality factor. In this case, Q increases up to 6200.
400
Amplifiers and Oscillators
10.3.3. Differential oscillator, Q increase, improvements The diagram of the improved oscillator is shown in Figure 10.15. The modifications consisted of the addition of two coils in the oscillator’s emitter circuits and two other coils in the amplifier’s collector circuit.
Figure 10.15. Differential oscillator, oscillating circuit, improved power and gain. For a color version of this figure, see www.iste.co.uk/dieuleveult/amplifiers.zip
The spectrum and phase noise in Figure 10.16 show that the output power is increased by 3 dB and that the noise floor is decreased by 5dB and goes to –160 dBc/Hz. This means that the noise factor was simultaneously decreased by 2 dB. Therefore, there are 5 dB of improvements distributed as follows: 3 dB in the power output and 2 dB in the noise factor.
Figure 10.16. Spectrum and phase noise, oscillating circuit, improved power and gain
Bonus Oscillators
401
We can also recalculate the value of Q in this condition if we assume that the frequency at which the phase noise reaches the noise floor is 50 kHz. This gives Q = 6200. This value concerns the entire LC network placed between the two collectors. However, at the same time, the phase noise at 1 kHz of the carrier was reduced by 3 dB and this was not the goal. If the circuit is dedicated to integration, the use of coils is preferably to be avoided. The summary given in Table 10.3 groups all of the characteristics of the two differential oscillators being compared. It is clearly seen that the phase noise and pushing, unsatisfactory in the first configuration, have been considerably improved with the transformation of the oscillating circuit. dBc/Hz Phase noise Tuning Frequency Pout 1 kHz 10 Pulling Pushing Harmonics Sensitivity MHz dBm kHz 100 MHz MHz/V dBc MHz/V kHz 1 MHz
Power supply Voltage Current (V) (mA)
FOM dBF
Basic oscillating circuit
625
-12
-90 -111 -
1.35
1200
10
-
5 3
5.0 .33
192
Enhanced oscillating circuit
625
-12
-144 -154
2.9
1.4
8
-
5 3
5.0 0.33
246
Table 10.3. A summary table of the basic differential oscillator and improved oscillating circuit
10.4. Differential oscillator SAW, improvements Equivalent tests, such as framing of the SAW with capacitive dividers, were engaged without any success. With the quality factor of the SAW filter being intrinsically high, it does not seem possible to envisage an improvement in this way. 10.5. Conclusion With a subject like oscillators, we could think of quickly arriving at conclusions. It has been shown here that it is always possible to explore new paths leading to an increased performance. Oscillators certainly still have room for improvement since the noise at 100 kHz of the carrier is still far from –174 dBc/Hz, which is the theoretical lower limit. Improvements in the choice of active component, noise factor or polarization point can most likely be considered.
402
Amplifiers and Oscillators
Knowing that most of the problem was based on the oscillating circuit’s quality factor, the adaptation of the impedance with the load as well as the active element’s noise factor were factors that were relatively unaddressed. These are new avenues to explore. Other improvements, such as the reduction of the supply voltage and the consumed current, as well as the rejection of harmonics, are to be explored in an attempt to increase the performance of these very promising structures.
Having spent countless days doing and redoing all of the demonstrations, recalculating all of the important parameters, performing and reperforming all of the simulations, examining the importance and the influence of each of the circuit’s parameters, it was then crucial to come up with a conclusion. Could we finally answer the fundamental question? Is there one and only one oscillator structure that outperforms all others? Part of the answer lies in the conclusions of Chapter 8, where we can fairly easily measure the supremacy of the series resonant Colpitts oscillator. As has been said over and over again, almost everything is based on the oscillating circuit’s quality factor. Leeson taught us the same thing in the form of his famous equation. Vackar, too, understood that in order to hide the harmful influence of the parasitic capacitances of the active element on the oscillating circuit, he had to insert a capacitive attenuator between the oscillating circuit and the amplifier. Another reflection is therefore necessary. It is useless and vain to want to separate Colpitts and Vackar. They are both right and their approach, consisting of favoring the oscillating circuit’s quality factor, is obviously the right one. Their approaches are not contradictory but complementary. A second thought comes next. Since Vackar’s way is proving to be wise, why not apply it to each side of the oscillating circuit, toward the source and the load? This amounts to placing a capacitive attenuator L on both sides of the oscillating circuit. Figure 10.1 represents these two oscillator topologies, which we decided to call Bora.
388
Amplifiers and Oscillators
Serial resonance
Parallel resonance
−G
C6
−G VE
C5
R
VE
L0 C0
C6
L0 C1
C3
C2
C4
VS
R1
C4
C2
C1
C5
R
C3
R1
VS
Figure 10.1. Topology of complementary oscillators, series or parallel resonance
In the diagram of Figure 10.1, the series or parallel resonant circuit is recognized, and then on either side of this circuit, we place two L-shaped capacitive attenuators. The computation having been carried out in the case of the Vackar oscillator, it is possible to directly apply the conclusions. The lower the values of capacitors C3 and C5 compared to C4 and C6, the better the efficiency of the L attenuators. In the case of the Vackar oscillator, the attenuation presented by the L attenuator must be compensated by the amplifier gain to satisfy the oscillation condition. In this final chapter, we therefore propose to examine the operation of these two oscillators only by the use of the simulator. The knowledge of the theoretical results of the Colpitts and Vackar oscillators is sufficient to realize the complete design of the oscillator without committing errors. The diagram in Figure 10.2 shows the first parallel resonance oscillator. Two successive transformations show that this oscillator is part of the series resonant Colpitts family. The first transformation is a star delta transposition that transforms PI attenuators into T attenuators. The second transformation groups capacitors C03 and C06. The set gives C0. We finally recognize the series resonant Colpitts oscillator framed by two capacitors. These two additional capacitors have an important role that is not limited to the suppression of the DC component. They intervene in phase noise, pulling and pushing.
Bonus Oscillators
−G VE
C5
R 1
C6
C05 C06
−G
L0
C3
C2 C1
C4
L0
C 03
R1
389
VS
C 04
R
C 01
C02
VE
R1
VS
2
C 05
−G
L0
C0
C04
R
C02
VE
C01
R1
VS
Figure 10.2. Successive transformation of the oscillator, parallel resonance
By placing a capacitive L-shaped elevator upstream of the resonant circuit, the attenuating effect of the capacitive divider placed downstream of the resonant circuit is annihilated. Without establishing the equations, or performing the calculation of the important oscillator parameters, we can realize that we will have all of the advantages and benefits envisaged by Vackar, without incurring the counterpart, which is a required increased gain. Since the oscillating circuit is placed between two symmetrical L-shaped circuits, it can be clearly seen that the oscillation frequency and oscillation condition will be identical to those which would be obtained without these two appendices upstream and downstream. We cannot say anything more without doing the calculation, as far as stability is concerned. 10.1. Parallel resonance oscillator The diagram of the Bora oscillator with parallel resonance is shown in Figure 10.3 along with the spectrum obtained in Transient simulation. This simulation is not necessary; its only role is to give information on the oscillation frequency.
390 Amplifiers and Oscillators
Figure 10.3. Transient simulation of the oscillator, parallel resonance
Bonus Oscillators
391
The design of this oscillator was limited to reproducing a Vackar oscillator to which was added an L capacitive divider. The most important and spectacular results are given by the Harmonic Balance simulation, the results of which are given in Figure 10.4.
Figure 10.4. Harmonic Balance simulation of the oscillator, parallel resonance
The oscillation frequency is 435.6 MHz. The spectrum in Figure 10.4 indicates that the power of the fundamental is approximately 0dBm and the second harmonic is rejected at 5.5 dB, which is not ideal. The results for phase noise are excellent, –136 dBc/Hz at 1 kHz of the carrier, then –155 dBc/Hz at 10 kHz and finally –167 dBc/Hz at 100 kHz. The circuit’s consumption is 4.3 mA under a supply voltage of 5 V, which leads us to an FOM of 235 dBF, which is quite respectable. We can then evaluate the oscillator’s pushing and pulling as has been done in all other cases. The results are shown in Figure 10.5; the pushing has a low value of 1.5 kHz/V. This value is at least 10 times lower than what is obtained in the best case. The pulling is also down by a factor of more than 10 compared to the best previous results, –0.7 kHz. The two capacitive attenuators placed on either side of the oscillating circuit perfectly played their role by considerably improving the phase noise, the FOM, the pushing and the pulling. The performance is compiled in Table 10.1. The results are comparable to those obtained with a SAW oscillator.
392
Amplifiers and Oscillators
Figure 10.5. Pushing and pulling simulation of the oscillator, parallel resonance
Frequency Pout MHz dBm 435
0
dBc/Hz Phase noise Pulling 1 kHz 10 kHz MHz 100 kHz 1 MHz -136 -155 -167
Pushing MHz/V
Harmonics dBc
1.5
5
-0.7
Tuning Power supply Sensitivity Voltage Current MHz/V (V) (mA) -
5
4.3
FOM dBF 235
Table 10.1. Summary table of oscillator performance, parallel resonance
This oscillator works perfectly when the supply voltage decreases to 3.3 V. The performances are preserved and the merit factor is always close to 235 dBF. To improve these performances, the two low-value capacitors C7 and C8, equal to 1pF in Figure 10.3, must be reduced, and this constitutes the major difficulty as these values are difficult to control. To facilitate the design of such an oscillator, it is sufficient to proceed in stages. The first stage consists of designing the basic oscillator, without the two capacitive L-shaped circuits. It is therefore a classic Colpitts oscillator. We can then simulate and record the oscillator’s performance. Finally, we add the two L-shaped capacitive circuits, chosen so that the ratios C7/C10 and C8/C9 are large, and the results are compared with those obtained previously. This design by stages proves that the design of such an oscillator is as simple as those found in all other cases. 10.2. Series resonant oscillator To design the series resonant oscillator, simply replace the coil with a coil in series with a capacitance. The lowest value is then given to the series capacitance, and then the value of the coil is calculated to obtain the desired frequency. This procedure maximizes the quality factor. The diagram of the Bora oscillator with series resonance is shown in Figure 10.6 along with the spectrum obtained in Transient simulation.
Bonus Oscillators
Figure 10.6. Transient simulation of the oscillator, series resonance
393
394
Amplifiers and Oscillators
The Transient simulation is not necessary, and, in any case, we must act with great care because the oscillator’s start-up time is quite long, in the order of a few milliseconds. If the simulation time is not long enough, the output level is measured during the start-up phase and the result does not make sense. There is nevertheless another piece of information which is quite reliable: the oscillation frequency, which is close to 473 MHz. HB shows that the oscillation frequency is 473.6 MHz. The spectrum in Figure 10.7 indicates that the power of the fundamental is approximately 0dBm and the second harmonic is rejected at 6.0 dB which, as in the previous case, is not ideal.
Figure 10.7. Harmonic Balance simulation of the oscillator, series resonance
The results for phase noise are excellent, –153 dBc/Hz at 1 kHz of the carrier, then –166 dBc/Hz at 10 kHz and finally –167 dBc/Hz at 100 kHz. The circuit’s consumption is 4.3mA under a supply voltage of 5 V, which leads us to an FOM of 253 dBF, which is perfect. It is still possible to gain some dB by optimizing the values of the circuit shown in Figure 10.6 but it seems impossible to cross the limit of 257 dBF, which is quite remarkable. We can then evaluate the pushing and pulling of the oscillator as has been done in all other cases. The results are shown in Figure 10.8; pushing and pulling have values that are at least 10 times lower than what was obtained in the previous case.
Bonus Oscillators
476.33662
m2
476.33660
m1 X= 4.500000 freq[::,1]=476.3365M
476.33658
395
476.33659m1 476.33658
m1 X= 45.00000 freq[::,1]=476.3366M
476.33657 476.33656
476.33656 476.33655 476.33654
m2 X= 5.500000 freq[::,1]=476.3366M
476.33652 476.33650m1
476.33654
m2 X= 55.00000 freq[::,1]=476.3365Mm2
476.33653 476.33652 476.33651
476.33648 4.5
4.6
4.7
4.8
4.9
5.0
5.1
5.2
5.3
5.4
45
5.5
46
47
48
49
50
51
52
53
54
55
X
X
Figure 10.8. Pushing and pulling simulation of the oscillator, series resonance
The pushing has a value of 0.11 kHz/V and the pulling, also down by a factor greater than 10 compared to the previous result, has a value of –0.07 kHz. The performances of this oscillator are grouped in Table 10.2. We are here in the presence of the best configuration that combines good performance with phase noise, pulling and pushing. Reconciling the ideas of Colpitts and Vackar is thus an excellent idea. Frequency Pout MHz dBm 476
0
dBc/Hz Phase noise Pulling MHz 1 kHz 10 kHz 100 kHz 1 MHz -153 -166 -167
-0.07
Pushing MHz/V
Harmonics dBc
0.11
6
Tuning Power supply Sensitivity Voltage Current MHz/V (V) (mA) -
5
4.3
FOM dBF 253
Table 10.2. Summary table of oscillator performance, series resonance
10.3. Differential oscillator, improvements It is questionable whether the solution of masking the drifts due to variations in parasitic capacitance for the introduction of a capacitive divider is applicable to other types of oscillators. We are particularly interested in the differential oscillator. During previous analyses, it was found that the differential oscillator had two major defects, a moderate phase noise and a very poor value of pushing. If the power is transmitted to the load via an auxiliary amplifier, the value of the pulling is satisfactory and this is the case of the oscillator shown in Figure 10.9. We therefore decided to repeat the diagram in Figure 10.9 and perform two tests, the first with a simple parallel resonant circuit connected between the two collectors and a second by interposing capacitive dividers.
396
Amplifiers and Oscillators
10.3.1. Differential oscillator, basic diagram The first tested oscillator corresponds to the diagram in Figure 10.9. The results of the first test are given in Figures 10.10 and 10.11. The output spectrum as well as the phase noise is given in Figure 10.10. The oscillation frequency is 625.2 MHz, the output level of the fundamental is –11.8 dBm, and the harmonics are, at best, rejected at 10 dBc. The phase noise at 1 kHz of the carrier is not exceptional and is equal to –90.7 dBc/Hz. Consumption is 5.4 mA, giving a merit factor of 192 dBF, which is quite ordinary.
Figure 10.9. Basic differential oscillator. For a color version of this figure, see www.iste.co.uk/dieuleveult/amplifiers.zip
Figure 10.10. Basic differential oscillator, spectrum and phase noise
Bonus Oscillators
397
Figure 10.11. Basic differential oscillator, pushing and pulling
With the phase noise curve shown in Figure 6.3, we have the value of the noise floor, equation [10.1], and the value of the frequency at which the phase noise joins the noise floor, equation [10.2]: −
=
− −
[10.1] = −174 +
=
−3− [10.2]
With the results shown in Figure 10.10, we have the noise floor which is –155 dBc/Hz and the frequency at which the phase noise joins the noise floor, 5 Mz. Knowing that the output power is –12 dBm, we can deduce a noise factor of 10 dB. Knowing that the oscillation frequency is 620 MHz, we deduce the quality factor Q = 62. These results show that it is likely that this oscillator can be improved by acting on the output power and on the noise factor. Figure 10.11 shows the result of pulling and pushing tests. An amplifier interposed between the oscillator and the output plays the role of isolation and provides an excellent pulling value, 1.35 kHz for a variation of 10 Ohms of the load. By contrast, the value of pushing is execrable and reaches 1.2 MHz/V and is similar to a control input of a VCO. By examining the schematic diagram of Figure 10.9, it can be seen that the two bases of the transistors constituting the oscillator are polarized by voltages of 3 V,
398
Amplifiers and Oscillators
which are assumed to be stabilized. In the pushing analysis, only the 5 V supply voltage is subject to variations. The influence of the parasitic base collector capacitances which, varying with the base collector voltage, act on the oscillation frequency is therefore measured. 10.3.2. Differential oscillator, Q increase Our goal, therefore, is to develop a circuit capable of masking the variations of the base collector capacitors. The idea is to transpose the previous structure and to insert capacitive dividers. These ideas are implemented in the diagram of Figure 10.12. Both capacitors C7 and C8 are of low value, 1pF, and capacitor C9 is of high value, 12pF. Two resistors R23 and R24 complement the device, as was the case in the improved Colpitts oscillator presented at the beginning of this chapter.
Figure 10.12. Differential oscillator with improved oscillating circuit. For a color version of this figure, see www.iste.co.uk/dieuleveult/amplifiers.zip
Here, the two additional capacitors constitute a current divider. The simulation results are given in Figure 10.13 for spectrum and phase noise and Figure 10.14 for pushing and pulling. The only difference between the diagrams in Figures 10.9 and 10.12 is the nature of the oscillating circuit connected between the two collectors of the oscillator. All other parameters are identical in terms of component values and operating point.
Bonus Oscillators
399
Figure 10.13. Basic differential oscillator, spectrum and phase noise
The spectrum shows that the output power is slightly diminished and goes to just under –12 dBm, a decrease of 0.4 dB. The rejection of harmonics is 8 dB at best; the result has deteriorated by approximately 2 dB. These two small disappointments are acceptable, compared to the performance on the phase noise which passes at –144 dBc/Hz at 1 kHz of the carrier and –154 dBc/Hz at 10 kHz of the carrier. The current drawn is unchanged, giving a remarkable merit factor of 246 dBF. The gain provided by the capacitive divider is considerable: 54 dB on the phase noise at 1 kHz of the carrier and 43 dB at 10 kHz of the carrier. The only criticism that can be made about this oscillator is the value of the phase noise floor of –155 dBc at 1 MHz of the carrier. This parameter can probably be improved. The values of pushing and pulling are given in Figure 10.14: 1.4 kHz/V for pushing and 2.9 kHz for pulling. The pushing has been improved by a factor of about 1000. This confirms the interest of the capacitive divider.
Figure 10.14. Differential oscillator with improved oscillating circuit, pushing and pulling
We can also calculate the apparent quality factor. In this case, Q increases up to 6200.
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Amplifiers and Oscillators
10.3.3. Differential oscillator, Q increase, improvements The diagram of the improved oscillator is shown in Figure 10.15. The modifications consisted of the addition of two coils in the oscillator’s emitter circuits and two other coils in the amplifier’s collector circuit.
Figure 10.15. Differential oscillator, oscillating circuit, improved power and gain. For a color version of this figure, see www.iste.co.uk/dieuleveult/amplifiers.zip
The spectrum and phase noise in Figure 10.16 show that the output power is increased by 3 dB and that the noise floor is decreased by 5dB and goes to –160 dBc/Hz. This means that the noise factor was simultaneously decreased by 2 dB. Therefore, there are 5 dB of improvements distributed as follows: 3 dB in the power output and 2 dB in the noise factor.
Figure 10.16. Spectrum and phase noise, oscillating circuit, improved power and gain
Bonus Oscillators
401
We can also recalculate the value of Q in this condition if we assume that the frequency at which the phase noise reaches the noise floor is 50 kHz. This gives Q = 6200. This value concerns the entire LC network placed between the two collectors. However, at the same time, the phase noise at 1 kHz of the carrier was reduced by 3 dB and this was not the goal. If the circuit is dedicated to integration, the use of coils is preferably to be avoided. The summary given in Table 10.3 groups all of the characteristics of the two differential oscillators being compared. It is clearly seen that the phase noise and pushing, unsatisfactory in the first configuration, have been considerably improved with the transformation of the oscillating circuit. dBc/Hz Phase noise Tuning Frequency Pout 1 kHz 10 Pulling Pushing Harmonics Sensitivity MHz dBm kHz 100 MHz MHz/V dBc MHz/V kHz 1 MHz
Power supply Voltage Current (V) (mA)
FOM dBF
Basic oscillating circuit
625
-12
-90 -111 -
1.35
1200
10
-
5 3
5.0 .33
192
Enhanced oscillating circuit
625
-12
-144 -154
2.9
1.4
8
-
5 3
5.0 0.33
246
Table 10.3. A summary table of the basic differential oscillator and improved oscillating circuit
10.4. Differential oscillator SAW, improvements Equivalent tests, such as framing of the SAW with capacitive dividers, were engaged without any success. With the quality factor of the SAW filter being intrinsically high, it does not seem possible to envisage an improvement in this way. 10.5. Conclusion With a subject like oscillators, we could think of quickly arriving at conclusions. It has been shown here that it is always possible to explore new paths leading to an increased performance. Oscillators certainly still have room for improvement since the noise at 100 kHz of the carrier is still far from –174 dBc/Hz, which is the theoretical lower limit. Improvements in the choice of active component, noise factor or polarization point can most likely be considered.
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Amplifiers and Oscillators
Knowing that most of the problem was based on the oscillating circuit’s quality factor, the adaptation of the impedance with the load as well as the active element’s noise factor were factors that were relatively unaddressed. These are new avenues to explore. Other improvements, such as the reduction of the supply voltage and the consumed current, as well as the rejection of harmonics, are to be explored in an attempt to increase the performance of these very promising structures.