CC BY
2СХЕМОТЕХНИКА И ПРОЕКТИРОВАНИЕ CIRCUIT ENGINEERING AND DESIGN
Original article УДК 621.382.049.58 doi:10.24151/1561-5405-2024-29-1-42-51 EDN: WFESBP
Optimization of the audio-frequency voltage-controlled oscillator
H. A. Babajanyan1'2, S. Kh. Khudaverdyan1
1National Polytechnic University of Armenia, Yerevan, Armenia 2 "Synopsys Armenia " CJSC, Yerevan, Armenia
babajany@synopsys.com
Abstract. The main working principle of voltage-controlled oscillator (VCO) circuits is based on self-generation of the output signal. The circuit components that enable self-oscillation can cause excess increase or decrease of the signal, resulting in amplitude noise. In the audio-frequency VCO, the standard capacitor or buffer can be used to reduce the noise. However, capacitor or buffer can modify the rise / fall time of the signal, which will lead to a change in the signal period. Additionally, these elements increase the circuit area. In this work, a new method for optimizing the audio-frequency VCO circuit is presented. The method is based on using, instead of an output operational amplifier, a simple circuit consisting of a Schmitt trigger and inverters and having smaller area compared to the operational amplifier. This makes it possible to get clear square signal. In addition, there is no need to use the resistors placed on the positive input of the operational amplifier. The folded cascode operational amplifier is used in the circuit. All other circuit components are the same as they were before the proposed method was used. It was demonstrated that the method under consideration lowers the output noise, allows the increase of the output characteristics linearity and the decrease of surface area of the audio-frequency VCO. It has been established that in the audio-frequency VCO designed in 32 nm technology, the noise is reduced by 30 %, the linearity error by 17 %, and the area by 28 %.
Keywords: voltage-controlled oscillator, Schmitt trigger, inverter, operational amplifier, resistor, capacitor
For citation: Babajanyan H. A., Khudaverdyan S. Kh. Optimization of the audiofrequency voltage-controlled oscillator. Proc. Univ. Electronics, 2024, vol. 29, no. 1, pp. 42-51. https://doi.org/10.24151/1561-5405-2024-29-1-42-51. - EDN: WFESBP.
© H. A. Babajanyan, S. Kh. Khudaverdyan, 2024
Научная статья
Оптимизация аудиочастотного генератора, управляемого напряжением
А. А. Бабаджанян1'2, С. Х. Худавердян1
1 Национальный политехнический университет Армении, г. Ереван, Армения
2«Синопсис Армения», г. Ереван, Армения babajany@synopsys.com
Аннотация. Основной принцип работы схем генератора, управляемого напряжением (ГУН), основан на самогенерации выходного сигнала. Компоненты схемы, которые делают возможным автоколебание сигнала, могут быть причиной избыточного увеличения или уменьшения сигнала, что ведет к шуму в сигнале. В случае аудиочастотного ГУН для минимизации шума можно использовать обычный конденсатор или инвертор. Однако конденсатор или инвертор могут изменить время нарастания / спада сигнала, что приведет к изменению периода сигнала. Кроме того, эти элементы увеличивают площадь схемы. В работе представлен новый метод для оптимизации схемы аудиочастотного ГУН. Метод основан на использовании вместо выходного операционного усилителя более простой схемы, состоящей из триггера Шмитта и инверторов и имеющей меньшую площадь по сравнению с операционным усилителем. Это дает возможность получать четкий прямоугольный сигнал. Также нет необходимости использовать резисторы, размещенные на положительном входе операционного усилителя. В схеме применен свернутый каскодный операционный усилитель. Все остальные составляющие схемы те же, что и до применения предлагаемого метода. Показано, что использование рассматриваемого метода снижает уровень выходных шумов, позволяет увеличить линейность выходной характеристики и уменьшить площадь контура аудиочас-тотного ГУН. Установлено, что в аудиочастотном ГУН, разработанном по 32-нм технологии, шумы уменьшаются на 30 %, ошибка линейности уменьшается на 17 %, а площадь сокращается на 28 %.
Ключевые слова: генератор, управляемый напряжением, триггер Шмитта, инвертор, операционный усилитель, резистор, конденсатор
Для цитирования: Бабаджанян А. А., Худавердян С. Х. Оптимизация аудиочастотного генератора, управляемого напряжением // Изв. вузов. Электроника. 2024. Т. 29. № 1. С. 42-51. https://doi.org/10.24151/1561-5405-2024-29-1-42-51. -EDN: WFESBP.
Introduction. There are a number of known types of voltage-controlled oscillator (VCO) circuits, for example, crystal oscillator, or LC circuit, or multivibrator, or RC-oscillator. In the basic VCO oscillator, when control voltage Vc increases above the nominal value the output frequency also increases. Inversely, the output frequency decreases at the decrease of Vc below the nominal value. There are two major categories of VCO: harmonic oscillators that produce sinusoidal output signal, and relaxation oscillators that generate a sawtooth or triangle waveform.
One of the most important issues for the VCO circuit is amplitude noise problem. In harmonic oscillators, the stability of noise frequency and temperature is better compared with relaxation oscillators. The disadvantage of harmonic oscillator is that it's not implemented in simple way for a monolithic IC. The common form of relaxation oscillator is a VCO with comparator, integrator, switch and Schmitt trigger. Generally, the operational amplifier (OpAmp) with input resistors and feedback resistor is used as a Schmitt trigger.
Literature review. There are several methods using the Schmitt trigger to improve the working process of oscillators. In [1], the optimization approach for the Schmitt trigger circuit is shown. The authors describe many properties and features of the Schmitt trigger and demonstrate its applicability. In [2], the Schmitt trigger is used to obtain a wider operating range for the digital-controlled oscillator (DCO), thus enabling the DCO to have segmental coarse-tuning and fine-tuning stages. Table 1 shows the power performance of different tuning stages and the path selector MUX.
Table 1
Power performance of different tuning stages and path selector MUX
Tuning stage Design Power 215 MHz Power 750 MHz
Coarse tuning Conventional 86.55 uW 245.75 uW
Proposed in [2] 77.21 uW 28.86 uW
Improvement percent 10.8 % 88.3 %
Path selector MUX Conventional 6.617 uW -
Proposed in [2] 3.91 uW -
Improvement percent 45.8 % -
Fine tuning Approach 1 465.92 uW -
Approach 2 207.64 uW -
Proposed in [2] 56.22 uW -
In [3], clean square signals are generated from noisy input signals using a Schmitt trigger in the current starved VCO circuit. This method also improves the working process of the phase-locked loop (PLL) circuit. The frequency ranges for different values of the control voltage set by the control mechanisms described in [3] are given below:
0.42 V..........................................152.89 MHz
0.6 V............................................686.01 MHz
0.8 V............................................1.315 GHz
1.0 V............................................1.7970 GHz
1.2 V............................................2.1819 GHz
1.4 V............................................2.4643 GHz
1.8 V............................................2.873 GHz
2.0 V............................................2.9971 GHz
2.2 V............................................3.0 GHz
2.4 V............................................3.134 GHz
2.6 V............................................3.2 GHz
2.8 V............................................3.2209 GHz
3.0 V............................................3.2406 GHz
In [4], a process, voltage, and temperature independent (PVT insensitive) Schmitt trigger with fully adjustable hysteresis is presented. The modifications done to the circuit make it more applicable for use in digital systems. The principle of the new method is the use of a Schmitt trigger circuit as part of an audio-frequency VCO circuit. That has been done for the first time on this circuit type. A performance comparison of the proposed method with other works is shown in table 2.
Table 2
Comparison of proposed method with other works
Referent Sources Proposed work
criterion [1] [2] [3] [4]
Consumed 3.4 uA q.5 mA N / A N / A 2.51 uA
current
Supply voltage 3 V 1 V 3.3 V 2 V 1 V
Power 10.2 uW 1.5 mW N / A N / A 2.51 uW
consumption
Process 180 nm 250 nm 130 nm 180 nm 130 nm
Signal fre- 1.25 Hz 2 MHz 133 MHz 50 Hz 5 MHz
quency
Application Sensing node Sensing node High-speed buffer Sensing node Sensing node
Structure Traditional Traditional Modified Inverter- Inverter-
open-loop comparator close-loop comparator traditional Schmitt trigger comparator based Schmitt trigger comparator based Schmitt trigger
Hysteresis Adjustable Fixed Fixed Adjustable Adjustable
PVT sensitivity Insensitive Sensitive Insensitive Insensitive Insensitive
In [5], the importance of the Schmitt trigger in low voltage CMOS oscillators is substantiated. The general dangers of amplitude noise are described in [6-9].
The proposed audio-frequency VCO circuit optimization. An experiment was conducted to improve the audio-frequency VCO circuit using a Schmitt trigger. In the primary circuit of the audio-frequency VCO (fig. 1, a), the output signal is formed by the large current flowing process in the inner circuit of the OpAmp and through the input and feedback loop resistors. The output signal is subject to noise and rise and fall times. Although noises can be removed by using a capacitor or inverter in the output, these components increase the circuit area and change the rise / fall time in the output, which leads to a change in the signal period.
The proposed method reduces amplitude noises, increases the linearity of output characteristics, and decreases the circuit area. Using a Schmitt trigger instead of the OpAmp with resistors allows the elimination of many known disadvantages. The size of the Schmitt trigger is chosen in a way that its high and low switching voltages match the high and low voltages of the triangle output of the first OpAmp in the primary audio-frequency VCO. Using a buffer after the Schmitt trigger is preferred to obtain a clear square signal. The Schmitt trigger has transistors whose sizes can be adjusted to make the high and low switching voltages more constant, resulting in more linear output characteristics for the audio-frequency VCO. Together, the Schmitt trigger and buffer occupy lesser area than the OpAmp with input and feedback loop resistors. The buffer provides an almost noiseless output signal: in the primary circuit output the noise error is 33 % and in the optimized circuit it is 3 %. The available sizes in the Schmitt trigger provide a more linear input voltage and output frequency dependency. The buffer also helps to make the output signal period more suitable for the output signal of the primary circuit. The optimized audio-frequency VCO is shown in fig. 1, b.
The condition that may be regarded as a disadvantage is that instead of using a ready-made OpAmp, it is necessary to determine the most suitable sizes for the Schmitt trigger to achieve the best possible performance for the audio-frequency VCO. Fig. 2 illustrates the real Schmitt trigger circuit.
Fig. 1. The primary (a) and optimized (b) circuits of audio-frequency VCO: 1 - OpAmp; 2 - Schmitt trigger; 3 - buffer
Increasing the W sizes of M6 and M2 transistors in the Schmitt trigger circuit makes it work more strictly, thereby enhancing the linearity of the audio-frequency VCO output characteristics.
Simulation results. The primary block of the audio-frequency VCO was designed and simulations carried out using the HSPICE simulator (as described in [10]) for several PVT corners, including TT, FF (fast-n fast-p), and SS (slow-n slow-p) processes with their respective voltage and temperature values. Simulation results given hereinafter are presented for the typical TT corner. The circuit was designed and simulated using the 32 nm technology, with input voltage ranging from 0.5 to 2.5 V and the output frequency ranging from 1.76 to 6.9 MHz. The primary circuit of the audio-frequency VCO designed using the 32 nm technology is shown in fig. 3, a, and the optimized circuit of audio-frequency VCO designed in this technology, in fig. 3, b.
Fig. 3. The primary (a) and optimized (b) circuits of audio-frequency VCO designed in 32 nm technology: 1 - OpAmp; 2 - Schmitt trigger; 3 - inverter
Fig. 4 shows the input and output signals of the second OpAmp used as Schmitt trigger in the primary circuit of audio-frequency VCO for input voltages of 0.5 and 2.5 V; fig. 5 shows the input and output signals of the real Schmitt trigger in the optimized circuit of audiofrequency VCO for the same input voltage values, and the combined output characteristics of the primary, optimized, and ideal audio-frequency VCO are shown in fig. 6.
Fig. 4. The triangle input signals in case of Vin = 0.5 V (Signal 1) and Vin = 2.5 V (Signal 2), and the square output signals in case of Vin = 0.5 V (Signal 3) and Vin = 2.5 V (Signal 4) of the second OpAmp used as Schmitt trigger in the primary circuit of audio-frequency VCO
Fig. 5. The triangle input signals in case of Vin = 0.5 V (Signal 1) and Vin = 2.5 V (Signal 2), and the square output signals in case of Vin = 0.5 V (Signal 3) and Vin = 2.5 V (Signal 4) of the real Schmitt trigger in the optimized circuit of audio-frequency VCO
Fig. 6. The combined output characteristics of the primary (1), optimized (2) and ideal (3) audio-frequency VCO circuits
Fig. 7. The Schmitt trigger circuit designed in 32 nm technology
Using the proposed method, it is possible to decrease the linearity error by 17 %, the noise error by 30 %, and the circuit area by 28 %. The noise error is calculated by dividing the additional voltage (noise amplitude) by the supply voltage and multiplying it by 100 %. The decrease of the linearity error was measured for the case in which the input voltage is equal to 1.5 V. This value was chosen for the measurement because it is the middle value where the linearity error is the highest. The decrease of the linearity error Linearity - errordecr is calculated by the following formula:
Linearity - errordecr = (fopt - fprim) / (fopt - fid) • 100 %,
where fopt is output frequency of the optimized audio-frequency VCO; fprim is output frequency of the primary audio-frequency VCO; fid is output frequency of the ideal audio-frequency VCO.
The circuit of the Schmitt trigger designed in 32 nm technology is shown in fig. 7, the combined input and output signals of the Schmitt trigger are shown in fig. 8, and the circuit of OpAmp designed in 32 nm technology is shown in fig. 9.
Fig. 8. The combined input (1) and output (2) signals of the Schmitt trigger
Fig. 9. The circuit of OpAmp designed in 32 nm technology
The gain of the folded cascade OpAmp designed in 32 nm technology is 52 dB, and the phase margin is -118°. Below are the sizes of the transistors used in the OpAmp:
xm12 vb2 vb2 vdd vdd p25 w = 2.442u l = 0.26u nf = 1 m = 1; xr4 vb4 iref vdd vdd p25 w = 30.86u l = 0.26u nf = 1 m = 4; xr3 iref iref vdd vdd p25 w = 8.46u l = 0.26u nf = 1 m = 4; xm13 net5 iref vdd vdd p25 w = 30.76u l = 0.26u nf = 1 m = 32; xm5 vout vb2 net1 vdd p25 w = 20.36u l = 0.26u nf = 1 m = 10; xm4 net23 vb2 net3 vdd p25 w = 20.36u l = 0.26u nf = 1 m = 10; xm3 net1 net23 vdd vdd p25 w = 11.76u l = 0.26u nf = 1 m = 1; xm2 net3 net23 vdd vdd p25 w = 11.76u l = 0.26u nf = 1 m = 1; xm1 net2 vinn net5 vdd p25 w = 45.05u l = 0.26u nf = 1 m = 25; xm0 net4 vinp net5 vdd p25 w = 45.05u l = 0.26u nf = 1 m = 25; xm14 vb1 iref vdd vdd p25 w = 11.76u l = 0.26u nf = 1 m = 4; xm11 vb2 vb4 vss vss n25 w = 3.41u l = 0.26u nf = 1 m = 1; xm10 vb4 vb4 vss vss n25 w = 3.85u l = 0.26u nf = 1 m = 1; xm9 net2 vb4 vss vss n25 w = 17.75u 1 = 0.26u nf = 1 m = 1; xm8 net4 vb4 vss vss n25 w = 17.75u l = 0.26u nf = 1 m = 1; xm7 vout vb1 net2 vss n25 w = 61.56u l = 0.61u nf = 1 m = 10; xm6 net23 vb1 net4 vss n25 w = 61.56u l = 0.61u nf = 1 m = 10; xm15 vb1 vb1 vss vss n25 w = 0.255u l = 0.26u nf = 1 m = 1.
The sizes of the Schmitt trigger are listed below:
xm2 vss vout net5 vdd p25 w = 0.36u l = 0.76u nf = 1 m = 1; xm1 vout vin net5 vdd p25 w = 15.36u l = 0.26u nf = 1q m = 1; xm0 net5 vin vdd vdd p25 w = 45.36u l = 0.26u nf = 1 m = 1; xm5 vdd vout net17 vss n25 w = 62.3u l = 0.26u nf = 1 m = 1; xm4 net17 vin vss vss n25 w = 1.36u l = 0.26u nf = 1 m = 1; xm3 vout vin net17 vss n25 w =4.36u l = 0.26u nf = 1 m = 1.
In the proposed configuration, a buffer consisting of 6 sequentially connected inverters is used. Alternatively, only 2 inverters can be used. However, in the case of 6 inverters, the output frequency of the optimized audio-frequency VCO is exactly the same as that of the primary audio-frequency VCO circuit for input voltages of 0.5 and 2.5 V.
The sizes of the inverter that comes after the Schmitt trigger are:
xm0 VOUT VIN VSS VSS n25 w = 75.36u l = 0.26u nf = 1 m = 1; xm1 VOUT VIN VDD VDD p25 w = 75.36u l = 0.26u nf = 1 m = 1.
Conclusion. A new method for the optimization of the audio-frequency VCO is proposed based on the principle of using a real Schmitt trigger and a buffer instead of an OpAmp with resistors in the positive input and feedback loop. High and low switching voltages of the Schmitt trigger were chosen appropriate to the high and low voltages of the triangle output signal of the first OpAmp. Thus the frequency range remains the same as in the primary circuit. The sizes of Schmitt trigger were chosen in order to obtain better linearity of output characteristics compared to primary circuit. In the audio-frequency VCO designed in 32 nm technology, the high switching voltage of Schmitt trigger is 2.4 V and the low switching voltage is 1.5 V. Input voltage changes from 0.5 to 2.5 V and output frequency range is 1.76-6.9 MHz. The following results have been obtained: linearity error of the output characteristics decreased by 17 %, noise error reduced by 30 % and the area of the circuit decreased by 28 %.
References
1. Shih-Lun C., Ming-Dou K. A new Schmitt trigger circuit in a 0.13-/spl mu/m 1/2.5-V CMOS process to receive 3.3-V input signals. IEEE Transactions on Circuits and Systems II: Express Briefs, 2005, vol. 52, no. 7, pp. 361-365. https://doi.org/10.1109/TCSII.2005.850409
2. Majd N. E., Lotfizad M., Ghaznavi-Ghoushchi M. B., Abadian A. An ultra low-power digitally controlled oscillator using novel Schmitt-trigger based hysteresis delay cells. IEICE Electronics Express, 2011, vol. 8, iss. 8, pp. 589-595. https://doi.org/10.1587/elex.8.589
3. Purnima, Radba B. L., Kumaraswamy K. V. VLSI design and implementation of Schmitt trigger based VCO for PLL architecture. International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, 2016, vol. 5, iss. 5, pp. 3547-3552.
4. Lin K., Wang X., Zhang X., Wang B., Ouyang T. A PVT-independent Schmitt trigger with fully adjustable hysteresis threshold voltages for low-power 1-bit digitization applications. IEICE Electronics Express, 2016, vol. 13, iss. 17, art. ID: 20160650. https://doi.org/10.1587/elex.13.20160650
5. Siniscalchi M. On the design of ultra low voltage CMOS oscillators, diss. for the Dr. Sci. (Electr. Eng.). Montevideo, 2020. xvi, 95 p.
6. Vibunjarone V., Prempraneerach Y. Improved noise reduction and frequency stability of VCO with external feedback loop. International Symposium on Nonlinear Theory and its Applications. Xi'an, IEICE, 2002, pp. 743-746.
7. Ozharar S., Ozdur I. Amplitude noise suppression by intracavity phase modulation in a harmonically mode-locked laser. Optics & Laser Technology, 2018, vol. 105, pp. 322-324. https://doi.org/10.1016/ j.optlastec.2018.02.033
8. Rossi C., Grigoli F., Gasperini P., Gandolfi S., Cocorullo C., Gukov T., Macini P. Estimation of amplitude noise reduction as a function of depth recorded by a deep vertical array (Northern Italy). EGU General Assembly 2023 (23-28 April, 2023, Vienna, Austria). Vienna, EGU, 2023. Art. ID: EGU23-1171. https://doi.org/ 10.5194/egusphere-egu23-1171
9. Tanaka A., Okamura Y., Takada A. Amplitude noise suppression of BPSK signals using transmission optical fibers and optical parametric phase-sensitive amplifiers. IEICE Electronics Express, 2022, vol. 19, iss. 13, art. no. 20220196. https://doi.org/10.1587/elex.19.20220196
10. HSPICE Application Manual. Synopsys Inc., 2010. 196 p.
The article was submitted 21.03.2023; approved after reviewing 31.07.2023;
accepted for publication 15.12.2023.
Information about the authors
Hayk A. Babajanyan - PhD student of the Electronics, Biomedicine and Measuring Devices Department, National Polytechnic University of Armenia (Armenia, 0009, Yerevan, Teryan st., 105), Engineer II, "Synopsys Armenia" CJSC (Armenia, 0026, Yerevan, Arshakunyats ave., 41), babajany@synopsys.com
Surik Kh. Khudaverdyan - Dr. Sci. (Eng.), Prof., Acting Head of the Communication Systems Department, National Polytechnic University of Armenia (Armenia, 0009, Yerevan, Teryan st., 105), xudaver13@mail.ru
