rus
Issue #6/2025
A. Yu. Kireev, A. A. Zhuravlev, A. V. Sosunov
Operating Point Bias Compensation Method for the Mach-Zehnder Modulator With Thermistors Circuit
Operating Point Bias Compensation Method for the Mach-Zehnder Modulator With Thermistors Circuit
DOI: 10.22184/1993-7296.FRos.2025.19.6.478.485
Mach-Zehnder microwave modulators on bulk or thin film lithium niobate are key components in data transmission networks, including quantum communications. However, the problem of operating point drift is still significant. A lot of methods for DC bias compensation for different technical tasks have been demonstrated. In this paper, we propose analog electrical scheme for thermal DC bias compensation using a thermistor system. We demonstrate the tuning of the electrical scheme for the operating point bias from temperature, and then experimentally confirm the effectiveness of this method by obtaining the maximum deviation from the mean optical power no more than 1.0 dB or 1.0 V applied DC voltage at temperature up to 45 °C. The proposed approach does not require any additional power supply for adjustment and can be used for special tasks in remote locations.
Mach-Zehnder microwave modulators on bulk or thin film lithium niobate are key components in data transmission networks, including quantum communications. However, the problem of operating point drift is still significant. A lot of methods for DC bias compensation for different technical tasks have been demonstrated. In this paper, we propose analog electrical scheme for thermal DC bias compensation using a thermistor system. We demonstrate the tuning of the electrical scheme for the operating point bias from temperature, and then experimentally confirm the effectiveness of this method by obtaining the maximum deviation from the mean optical power no more than 1.0 dB or 1.0 V applied DC voltage at temperature up to 45 °C. The proposed approach does not require any additional power supply for adjustment and can be used for special tasks in remote locations.
Теги: dc bias drift electrical scheme mz-modulator operating point thermistors дрейф модулятор маха-цендера рабочая точка смещение по постоянному току терморезисторы электрическая схема
Operating Point Bias Compensation Method for the Mach-Zehnder Modulator With Thermistors Circuit
A. Yu. Kireev1, A. A. Zhuravlev1, A. V. Sosunov2
Perm Scientific Industrial Instrument-Making Company, Perm, Russia
Perm State University, Perm, Russia
Mach-Zehnder microwave modulators on bulk or thin film lithium niobate are key components in data transmission networks, including quantum communications. However, the problem of operating point drift is still significant. A lot of methods for DC bias compensation for different technical tasks have been demonstrated. In this paper, we propose analog electrical scheme for thermal DC bias compensation using a thermistor system. We demonstrate the tuning of the electrical scheme for the operating point bias from temperature, and then experimentally confirm the effectiveness of this method by obtaining the maximum deviation from the mean optical power no more than 1.0 dB or 1.0 V applied DC voltage at temperature up to 45 °C. The proposed approach does not require any additional power supply for adjustment and can be used for special tasks in remote locations.
Keywords: MZ-modulator, DC bias, drift, operating point, thermistors, electrical scheme
Article received:20.07.2025
Article accepted: 14.08.2025
Introduction
Mach-Zehnder microwave modulators (MZ-modulator) are widely used devices in telecommunication systems [1, 2], sensors [3] and quantum networks [4, 5].
The work principle of the microwave Mach-Zehnder modulator is to change the amplitude of the optical signal under the electro-optic effect (Fig. 1). The maximum amplitude is observed in the case of constructive interference, and the minimum amplitude – destructive interference. The transfer function of the MZ-modulator is nonlinear and has the form of a cosine wave. The MZ-modulators on lithium niobate (LN) are widely employed owing to its high speed, low driving voltage, low transmission loss, zero chirp and high bandwidth.
Microwave MZ-modulators on bulk lithium niobate crystals are well studied and used in industry (frequency band is limited to 40 GHz) [6]. At the same time, microwave modulators on thin film LN demonstrate great progress in scientific research (frequency band up to 100 GHz) [7]. However, both types of MZ-modulators have the problem of direct current bias (DC bias) point drift due to applied electric field or temperature [8–10]. The DC bias of operating point is caused by both the nature of the LN crystal (free-charges [10]) and design features (buffer layers [11,12], electrodes, etc.) of MZ-modulators. In general, to the DC bias compensate, it is necessary to influence both the LN structure and the MZ-modulator design. There is currently no universal method.
Several methods have been proposed to modify the LN surface structure to the DC bias reduce, such as temperature pre-annealing [13–15], high-energy Ar+ ion milling preprocessing [16] and thin film deposition [17]. On the other hand, most approaches are devoted to the design of MZ-modulators. Various feedback methods are proposed to compensate for DC bias to keep the operating point in the quadrature point [18–20]. For example, a feedback method is proposed to control the bias voltage by mathematical model and fast Fourier transform analysis [21]. Basically, these methods require sophisticated circuits and a lot of power supply. A method has been proposed to largely reduce bias power consumption by combining passive bias and thermo-optic bias [22]. This technique can facilitate the development of practical high-speed MZ-modulators on the lithium niobate platform. Thus, methods for reducing the operating point drift that do not require much electrical power are an important practical task. Such decisions are important for increasing the stability of MZ-modulators for remote locations. The aim of this work is DC bias thermal compensation of the MZ-modulator by thermistors circuit for use in remote locations without a power supply.
Experiment
First, the temperature drift of the operating point of MZ-modulator was calculated (Fig. 2). For this task, linearly polarized light from a narrow-band laser at 1 550 nm (1) was formed using a polarization controller (2). Then, the operating point of the MZ-modulator (7) was set in the quadrature point using a power supply (4). The amplitude level of the optical signal was controlled using an optical power meter (6). Heating in the thermal chamber (8) was performed from 0 to 45 °C with a step of 5 °C and 40 min hold at each step. DC bias of the operating point of the MZ-modulator during heating was compensated by applying a constant voltage using a power supply. The voltage was controlled by using a multimeter (5). This made it possible to empirically establish the functional relationship between the temperature and the DC bias voltage of the MZ-modulator (correlation function).
Secondly, an intelligent analog electrical circuit based on temperature-sensitive resistors (3) was developed to automate the thermal compensation process. The electrical circuit consists of two thermistors (pre-calibrated), which provide an accurate reproduction of the previously obtained correlation function. This approach eliminates the need for manual adjustment of the system, maintaining the stability of optical power with temperature fluctuations and constant input voltage.
Results and Discussion
A. MZ-modulator Characterization
All parameters of the MZ-modulator are given in Table. The transfer function of the MZ-modulator is given in Fig. 3. The transfer function is described by the follow equation:
Pout = 1 + cos − ψ, (1)
where Pout – output optical power, Pin – input optical power, ψ – phase, V – voltage, Vπ – half-wave voltage.
The optical power of MZ-modulator was analyzed by a spectroanalyzer Yokogawa AQ6375B to reconstruct the transfer function. The voltage at the DC electrodes (DC signal) was varied in the range of 0–16 V with a step of 0.5 V by power supply.
B. Thermistor Circuit Model Calculation
The task was to select a simple non-volatile electrical circuit based on two thermistors for a specific MZ-modulator. Such ideas, which offer a specific model for the MZ-modulator, are considered promising [21]. First, we realized temperature measurements of the MZ-modulator in the range of 0–45 °C and determined DC bias. The DC bias is compensated by applying voltage. We experimentally calculated this voltage to keep the operating point in the quadrature point when the temperature changes (Fig. 4a, red line). We then used this result to select the nominal resistance of the resistors in electrical circuit (Fig. 4b) to compensate for MZ-modulator temperature drift. The electrical circuit and calculation of the resistance of the resistors are given equations (2)-(3):
Vout = . (2)
For simplicity, let’s assume R1 = R2, then
Vout = . (3)
since R4, R3 is constant, we selected the resistor values using a mathematical model (R4 = 960 Ohm, R3 = 2 300 Ohm, R1 = R2 = 10 350 Ohm at 25 °С). The calculated parameters of the thermistors according to equations (2–3) made it possible to obtain a theoretical curve for the MZ-modulator (Fig. 4a, blue line).
The theoretical and experimental results demonstrate a high degree of consistency, which confirms the adequacy of the model of the electrical circuit for compensating the offset of the operating point of the MZ-modulator. In order to improve the performance characteristics of the electrical circuit, it is of interest to realize a scalable architecture involving the introduction of additional thermoresistive elements. This will allow to expand the range of nonlinear correction and increase the accuracy of compensation of the temperature drift of the operating point of the MZ-modulator.
At the same time, the achievement of high metrological characteristics of the electrical circuit is possible only under the condition of stability and reproducibility of the nonlinear transfer function of the amplitude MZ-modulator. Thus, the accuracy performance of the whole system is determined not only by the parameters of the electrical circuit itself, but also by the quality of repeatability of the characteristics of the MZ-modulator in different temperature regimes and cycles of operation.
At this stage, the implemented electrical circuit for DC bias compensation of the operating point demonstrates satisfactory accuracy characteristics. The achievable degree of temperature drift compensation and maintenance of the specified operating mode of the MZ-modulator meets the specified technical requirements, which allows us to consider the device as functionally complete and suitable for further optimization and practical application.
C. MZ-modulator Temperature Compensation
The experiment confirmed that an electrical circuit based on thermistors successfully compensates for the DC bias of the MZ- modulator due to the temperature changes. The output optical power changed in the range of 1 dBm with the temperature increase to 45 °C (Fig. 5a). In this case, the voltage Vout increased linearly in the range from 0 to 1 V from the value of the operating point from temperature (Fig. 5b).
One of the key advantages of DC bias compensation of the operating point using thermistors is the autonomy of the electrical circuit due to the absence of the need for external power supplies. This makes it possible to realize a non-volatile and self-regulating parameter correction system, which is especially important in conditions of limited access to electrical energy or in the design of low-consumption devices.
In addition, the simplicity analog scheme, eliminates the need for digital signal processing blocks. This factor not only reduces the overall complexity of the design, but also minimizes the probability of errors related to software, discrete processing algorithms or time synchronization. Thus, high reliability of the device operation in a wide range of operating conditions is achieved.
One of the significant disadvantages of this approach is the complexity of parametric tuning associated with the accurate selection of thermistor ratings. This is due to the requirement to provide a high degree of agreement between the resistance of the thermistor and the operating voltage of the MZ modulator when the temperature changes. Nonlinearity of thermistor characteristics and variation of MZ modulator parameters requires an individual approach and considerable time expenditures. Extension of the temperature range of the electrical circuit operation (negative temperatures) seems theoretically feasible. However, the practical realization of this idea is largely determined by the response parameters of the amplitude MZ modulator, their predictability and reproducibility. This study will be carried out in the next paper. The nonlinear transfer function of the MZ modulator when the temperature drops below zero can have a significant effect on the compensation efficiency, which requires additional analysis and adaptation of circuit solutions.
Conclusion
In this paper, we proposed an analog method for compensating DC bias of the operating point of MZ-modulators using an electrical circuit with thermistors. The results can be used in practice in remote areas where there are difficulties in delivering electrical energy. The proposed method can be improved by using a larger number of thermistors and expanding the temperature range, which is planned for future work.
Acknowledgements
We are grateful to prof. V. A. Demin for proofreading and discussion.
Funding
This work was funded by state assignment FSNF‑2024–0001
Data availability statement
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
AUTHORS
Sosunov Aleksei Vladimirovich : Cand. of Sc.(Tech.), Senior Researcher, Perm State University, Perm, Russia, e-mail: avsosunov@psu.ru
ORCID 0000-0002-5760-1523
Kireev Arseny Yurievich: Research Engineer, Perm Scientific Industrial Instrument-Making Company, Perm, Russia, e-mail:Kireev@pnppk.ru
ORCID: 0009-0002-6792-7823
Zhuravlev Anton Aleksandrovich: Cand. of Sc. (Tech.), head of scientific-research institute of photonics and optoelectronics, Perm Scientific Industrial Instrument-Making Company, Perm, Russia, e-mail: aaz@pnppk.ru
ORCID: 0000-0003-2270-6314
Conflicts of Interest
The authors declare no conflicts of interest.
CREDIT AUTHOR STATEMENT
Arseny Kireev: Formal analysis, Data curation, Investigation, Writing-Original Draft; Anton Zhuravlev: Conceptualization, Resources, Supervision; Aleksei Sosunov; Visualization, Writing-Original Draft, Funding acquisition.
A. Yu. Kireev1, A. A. Zhuravlev1, A. V. Sosunov2
Perm Scientific Industrial Instrument-Making Company, Perm, Russia
Perm State University, Perm, Russia
Mach-Zehnder microwave modulators on bulk or thin film lithium niobate are key components in data transmission networks, including quantum communications. However, the problem of operating point drift is still significant. A lot of methods for DC bias compensation for different technical tasks have been demonstrated. In this paper, we propose analog electrical scheme for thermal DC bias compensation using a thermistor system. We demonstrate the tuning of the electrical scheme for the operating point bias from temperature, and then experimentally confirm the effectiveness of this method by obtaining the maximum deviation from the mean optical power no more than 1.0 dB or 1.0 V applied DC voltage at temperature up to 45 °C. The proposed approach does not require any additional power supply for adjustment and can be used for special tasks in remote locations.
Keywords: MZ-modulator, DC bias, drift, operating point, thermistors, electrical scheme
Article received:20.07.2025
Article accepted: 14.08.2025
Introduction
Mach-Zehnder microwave modulators (MZ-modulator) are widely used devices in telecommunication systems [1, 2], sensors [3] and quantum networks [4, 5].
The work principle of the microwave Mach-Zehnder modulator is to change the amplitude of the optical signal under the electro-optic effect (Fig. 1). The maximum amplitude is observed in the case of constructive interference, and the minimum amplitude – destructive interference. The transfer function of the MZ-modulator is nonlinear and has the form of a cosine wave. The MZ-modulators on lithium niobate (LN) are widely employed owing to its high speed, low driving voltage, low transmission loss, zero chirp and high bandwidth.
Microwave MZ-modulators on bulk lithium niobate crystals are well studied and used in industry (frequency band is limited to 40 GHz) [6]. At the same time, microwave modulators on thin film LN demonstrate great progress in scientific research (frequency band up to 100 GHz) [7]. However, both types of MZ-modulators have the problem of direct current bias (DC bias) point drift due to applied electric field or temperature [8–10]. The DC bias of operating point is caused by both the nature of the LN crystal (free-charges [10]) and design features (buffer layers [11,12], electrodes, etc.) of MZ-modulators. In general, to the DC bias compensate, it is necessary to influence both the LN structure and the MZ-modulator design. There is currently no universal method.
Several methods have been proposed to modify the LN surface structure to the DC bias reduce, such as temperature pre-annealing [13–15], high-energy Ar+ ion milling preprocessing [16] and thin film deposition [17]. On the other hand, most approaches are devoted to the design of MZ-modulators. Various feedback methods are proposed to compensate for DC bias to keep the operating point in the quadrature point [18–20]. For example, a feedback method is proposed to control the bias voltage by mathematical model and fast Fourier transform analysis [21]. Basically, these methods require sophisticated circuits and a lot of power supply. A method has been proposed to largely reduce bias power consumption by combining passive bias and thermo-optic bias [22]. This technique can facilitate the development of practical high-speed MZ-modulators on the lithium niobate platform. Thus, methods for reducing the operating point drift that do not require much electrical power are an important practical task. Such decisions are important for increasing the stability of MZ-modulators for remote locations. The aim of this work is DC bias thermal compensation of the MZ-modulator by thermistors circuit for use in remote locations without a power supply.
Experiment
First, the temperature drift of the operating point of MZ-modulator was calculated (Fig. 2). For this task, linearly polarized light from a narrow-band laser at 1 550 nm (1) was formed using a polarization controller (2). Then, the operating point of the MZ-modulator (7) was set in the quadrature point using a power supply (4). The amplitude level of the optical signal was controlled using an optical power meter (6). Heating in the thermal chamber (8) was performed from 0 to 45 °C with a step of 5 °C and 40 min hold at each step. DC bias of the operating point of the MZ-modulator during heating was compensated by applying a constant voltage using a power supply. The voltage was controlled by using a multimeter (5). This made it possible to empirically establish the functional relationship between the temperature and the DC bias voltage of the MZ-modulator (correlation function).
Secondly, an intelligent analog electrical circuit based on temperature-sensitive resistors (3) was developed to automate the thermal compensation process. The electrical circuit consists of two thermistors (pre-calibrated), which provide an accurate reproduction of the previously obtained correlation function. This approach eliminates the need for manual adjustment of the system, maintaining the stability of optical power with temperature fluctuations and constant input voltage.
Results and Discussion
A. MZ-modulator Characterization
All parameters of the MZ-modulator are given in Table. The transfer function of the MZ-modulator is given in Fig. 3. The transfer function is described by the follow equation:
Pout = 1 + cos − ψ, (1)
where Pout – output optical power, Pin – input optical power, ψ – phase, V – voltage, Vπ – half-wave voltage.
The optical power of MZ-modulator was analyzed by a spectroanalyzer Yokogawa AQ6375B to reconstruct the transfer function. The voltage at the DC electrodes (DC signal) was varied in the range of 0–16 V with a step of 0.5 V by power supply.
B. Thermistor Circuit Model Calculation
The task was to select a simple non-volatile electrical circuit based on two thermistors for a specific MZ-modulator. Such ideas, which offer a specific model for the MZ-modulator, are considered promising [21]. First, we realized temperature measurements of the MZ-modulator in the range of 0–45 °C and determined DC bias. The DC bias is compensated by applying voltage. We experimentally calculated this voltage to keep the operating point in the quadrature point when the temperature changes (Fig. 4a, red line). We then used this result to select the nominal resistance of the resistors in electrical circuit (Fig. 4b) to compensate for MZ-modulator temperature drift. The electrical circuit and calculation of the resistance of the resistors are given equations (2)-(3):
Vout = . (2)
For simplicity, let’s assume R1 = R2, then
Vout = . (3)
since R4, R3 is constant, we selected the resistor values using a mathematical model (R4 = 960 Ohm, R3 = 2 300 Ohm, R1 = R2 = 10 350 Ohm at 25 °С). The calculated parameters of the thermistors according to equations (2–3) made it possible to obtain a theoretical curve for the MZ-modulator (Fig. 4a, blue line).
The theoretical and experimental results demonstrate a high degree of consistency, which confirms the adequacy of the model of the electrical circuit for compensating the offset of the operating point of the MZ-modulator. In order to improve the performance characteristics of the electrical circuit, it is of interest to realize a scalable architecture involving the introduction of additional thermoresistive elements. This will allow to expand the range of nonlinear correction and increase the accuracy of compensation of the temperature drift of the operating point of the MZ-modulator.
At the same time, the achievement of high metrological characteristics of the electrical circuit is possible only under the condition of stability and reproducibility of the nonlinear transfer function of the amplitude MZ-modulator. Thus, the accuracy performance of the whole system is determined not only by the parameters of the electrical circuit itself, but also by the quality of repeatability of the characteristics of the MZ-modulator in different temperature regimes and cycles of operation.
At this stage, the implemented electrical circuit for DC bias compensation of the operating point demonstrates satisfactory accuracy characteristics. The achievable degree of temperature drift compensation and maintenance of the specified operating mode of the MZ-modulator meets the specified technical requirements, which allows us to consider the device as functionally complete and suitable for further optimization and practical application.
C. MZ-modulator Temperature Compensation
The experiment confirmed that an electrical circuit based on thermistors successfully compensates for the DC bias of the MZ- modulator due to the temperature changes. The output optical power changed in the range of 1 dBm with the temperature increase to 45 °C (Fig. 5a). In this case, the voltage Vout increased linearly in the range from 0 to 1 V from the value of the operating point from temperature (Fig. 5b).
One of the key advantages of DC bias compensation of the operating point using thermistors is the autonomy of the electrical circuit due to the absence of the need for external power supplies. This makes it possible to realize a non-volatile and self-regulating parameter correction system, which is especially important in conditions of limited access to electrical energy or in the design of low-consumption devices.
In addition, the simplicity analog scheme, eliminates the need for digital signal processing blocks. This factor not only reduces the overall complexity of the design, but also minimizes the probability of errors related to software, discrete processing algorithms or time synchronization. Thus, high reliability of the device operation in a wide range of operating conditions is achieved.
One of the significant disadvantages of this approach is the complexity of parametric tuning associated with the accurate selection of thermistor ratings. This is due to the requirement to provide a high degree of agreement between the resistance of the thermistor and the operating voltage of the MZ modulator when the temperature changes. Nonlinearity of thermistor characteristics and variation of MZ modulator parameters requires an individual approach and considerable time expenditures. Extension of the temperature range of the electrical circuit operation (negative temperatures) seems theoretically feasible. However, the practical realization of this idea is largely determined by the response parameters of the amplitude MZ modulator, their predictability and reproducibility. This study will be carried out in the next paper. The nonlinear transfer function of the MZ modulator when the temperature drops below zero can have a significant effect on the compensation efficiency, which requires additional analysis and adaptation of circuit solutions.
Conclusion
In this paper, we proposed an analog method for compensating DC bias of the operating point of MZ-modulators using an electrical circuit with thermistors. The results can be used in practice in remote areas where there are difficulties in delivering electrical energy. The proposed method can be improved by using a larger number of thermistors and expanding the temperature range, which is planned for future work.
Acknowledgements
We are grateful to prof. V. A. Demin for proofreading and discussion.
Funding
This work was funded by state assignment FSNF‑2024–0001
Data availability statement
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
AUTHORS
Sosunov Aleksei Vladimirovich : Cand. of Sc.(Tech.), Senior Researcher, Perm State University, Perm, Russia, e-mail: avsosunov@psu.ru
ORCID 0000-0002-5760-1523
Kireev Arseny Yurievich: Research Engineer, Perm Scientific Industrial Instrument-Making Company, Perm, Russia, e-mail:Kireev@pnppk.ru
ORCID: 0009-0002-6792-7823
Zhuravlev Anton Aleksandrovich: Cand. of Sc. (Tech.), head of scientific-research institute of photonics and optoelectronics, Perm Scientific Industrial Instrument-Making Company, Perm, Russia, e-mail: aaz@pnppk.ru
ORCID: 0000-0003-2270-6314
Conflicts of Interest
The authors declare no conflicts of interest.
CREDIT AUTHOR STATEMENT
Arseny Kireev: Formal analysis, Data curation, Investigation, Writing-Original Draft; Anton Zhuravlev: Conceptualization, Resources, Supervision; Aleksei Sosunov; Visualization, Writing-Original Draft, Funding acquisition.
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