Pulsed microwave photonic vector network analyzer based on direct sampling

Min Ding; Xiaoen Chen; Zhengtao Jin; Jianping Chen; Guiling Wu

doi:10.1364/OE.480218

1. Introduction

As the essential test instrumentation in the microwave industry, vector network analyzers (VNAs) provide a clear understanding of the operation and performance in RF design and manufacturing [1]. A VNA usually conducts the scattering parameter (S-parameter) measurements with a continuous stimulation applied to a device under test (DUT). However, it would be more appropriate to utilize a pulse stimulation for active devices operating in pulsed mode, such as amplifiers, multipliers, and mixers in the pulsed radar system. In addition to device level test, pulsed measurement is also widely used for on wafer test to effectively prevent the DUT from overheating damage caused by the rapid temperature increase [2–7].

In the pulsed S-parameter measurement, the DUT is driven with a pulsed stimulation or biased with a pulsed power supply, and outputs the corresponding pulsed response. At each test frequency point, the spectral energy of the pulsed signal will spread across a wide bandwidth as the pulse width decreases, which sets a stringent requirement to the pulsed VNA to receive a wideband signal. Wideband detection and narrowband detection methods have been developed for conventional pulsed VNAs, respectively [8]. In wideband detection, data acquisition is synchronized with the pulsed signal to record data while the pulse turns on. Wideband detection is applicable when the majority of the pulsed signal spectrum falls within the bandwidth of the receiver. However, as the pulse width decreases, more spectrum energy spreads out of the receiver’s bandwidth so that the pulsed signal cannot be properly detected. M. Marchetti et al. proposed a solution to improve wideband detection method by increasing the intermediate frequency bandwidth and data acquisition rate [9]. Nevertheless, as the pulse width decreases, the number of acquired data in one pulse duration is very limited, affecting the measurement quality. To overcome the bandwidth limitation, narrowband detection with asynchronized data acquisition is introduced to capture the central frequency component and remove the other ones. However, this method will lead to the pulse desensitization phenomenon, where system dynamic range is reduced as the function of 20log(duty cycle) in dB.

In recent years, microwave photonics have attracted many attentions for providing a new perspective to break through limitations of electronic devices and systems [10,11]. Taking advantage of the large bandwidth, high accuracy and interference immunity of photonics, electrical measurements are further boosted by microwave photonic techniques [12–14].

In this paper, we propose a pulsed microwave photonic vector network analyzer (p-MPVNA) based on direct sampling. The proposed p-MPVNA features a broad system bandwidth [15] and optical undersampling to implement the asynchronous wideband detection with vector superposition. The broad system bandwidth can capture the wide spectrum of the pulsed signal, and the continuous spectrum is discretized into multiple frequency components and aliased down after asynchronously optical undersampling. Since the energy of the pulse signal is concentrated in the main lobe, the frequency components in the main lobe are recovered by digital signal processing and vector superimposed to extract pulsed S-parameters. The asynchronous wideband detection can mitigate the desensitization phenomenon, and the system dynamic range decreases as 10log(duty cycle) when pulse duty cycle is below 10$\%$, which is half slower than that of narrowband detection method. The pulsed S-parameter measurement principle and the system structure of the p-MPVNA are introduced in the second section. The experimental p-MPVNA is presented to verify the principle and system performance. A pulsed microwave amplifier is measured as an active device under test with different gain curves in the continuous and pulsed operation. The results are compared with the measurement from a commercial VNA. A low pass filter is measured as a DUT to demonstrate the dynamic range decrease with duty cycle.

2. Principle of the pulsed microwave photonic vector network analyzer

The structure of the proposed p-MPVNA is demonstrated in Fig. 1. In this scheme, a pulsed single tone signal generated by a signal generator (SG) is sent to the test set (TS), and divided into two routes, one as the reference signal and the other as the incident signal to stimulate the DUT. The reference signal and the corresponding response signals (reflected and transmitted signals) are fed into the four-channel optical direct sampling receiver (ODSR). The single channel structure of the ODSR is shown in the blue frame. In each channel, the input pulsed signal is directly sampled by an optical pulse train thru an electro-optic modulator (EOM). The sampling process is asynchronous with the pulsed signal, i.e. sampling is performed whether the pulse is on or off. The sampled signal is quantized by the optical intensity digitizer (OID) and the digitized signal is sent to the digital signal processing (DSP) module for calculation.

Fig. 1. (a) The scheme of the proposed p-MPVNA. SG: Signal generator; TS: Test set; DUT: Device under Test; ODSR: Optical direct sampling receiver; EOM: Electro-Optic modulator; OID: Optical intensity digitizer; DSP: Digital signal processing. (b) Pulsed single tone signal in time domain. (c) Pulsed single tone signal in frequency domain.

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The pulsed single tone signal incident to the DUT as shown in the Fig. 1(b) can be expressed as

(1)$$v_p(t) = v_{0}(t)\sum_{k={-}\infty}^{\infty}{\rm rect}(t-kT_p),$$

where $v_{0}(t)$ represents a single tone signal, and

(2)$${\rm rect}(t) =\left \{ \begin{array}{l} 1, -\tau/2+\triangle t < t < \tau/2+\triangle t\\ 0, {\rm others} \end{array} \right.,$$

represents a rectangular pulse with pulse width $\tau$. The period of the rectangular pulse train is $T_p$, and $0<\triangle t<T_p$ determines the signal starting timing. The response signals from the DUT can be written as

(3)$$v_{p}^{'}(t) = v_p(t)*s_{ij}(t),$$

where $s_{ij}(t)$ is the time domain impulse response of the DUT to the pulse single tone signal, the $i,j$ subscripts stand for the output and input ports respectively, and the asterisk operator, $*$, represents the convolution operation. Since $v_p(t)$ and $v_p^{'}(t)$ are both pulsed single tone signals sent to the receiver, they are denoted as $v_I(t)$. The corresponding frequency spectrum of $v_I(t)$ depicted in Fig. 2 can be derived as

(4)$$\begin{aligned} V_I(\Omega) = \frac{2\pi^2\tau A}{T_p}[\sum_{k={-}\infty}^{\infty}{\rm sinc}(\frac{\pi k\tau}{T_p})\delta(\Omega-\Omega_0-\frac{2\pi k}{T_p})e^{j\phi}&\\ +\sum_{k={-}\infty}^{\infty}{\rm sinc}(\frac{\pi k\tau}{T_p})\delta(\Omega+\Omega_0-\frac{2\pi k}{T_p})e^{{-}j\phi}],& \end{aligned}$$

where $A$, $\phi$ and $\Omega _0$ is the magnitude, phase and the analog angular frequency of the single tone signal. From Eq. (4) and Fig. 2, one can see the spectrum of $v_I(t)$ consists of a series of spectral lines, whose envelope is described as a ${\rm sinc}(\cdot )$ function. The interval of the spectral lines is set by the rectangular pulse period $T_p$ while the shape of the envelope is determined by the pulse width $\tau$.

Fig. 2. The equivalent model of the pulsed signal reception

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The optical pulse train in the ODSR is expressed as

(5)$$p(t) = P_A\sum_{n={-}\infty}^{\infty}p_s(t-nT_s),$$

where $P_A$ is the average power of the optical pulse train, $p_s(t)$ represents the normalized temporal contour of a single optical pulse and $T_s$ is the period of the optical pulse train. Mach-Zender modulator (MZM) is commonly used as the EOM. With a small input signal, the optical pulse train asynchronously samples $v_I(t)$ thru the quadrature biased MZM. The sampling time continues for multiple pulse periods to discretize the signal spectrum. Then the OID generally including a photodetector (PD) and an analog to digital convertor (ADC) operate linearly to quantize the peak value of each optical pulse, and the digitized signal can be obtained

(6)$$v_Q[n] = v_{Q0}[n]+v_{Q1}[n],$$

where $v_{Q0}[n]$ is a constant, $v_{Q1}[n]=\left. h_A(t)*v_I(t) \right |_{t=nT_s}$ carries the desired pulsed signal $v_I(t)$, and $h_A(t)$ is the equivalent system impulse response. The pulsed S-parameters, defined as the complex ratio of the pulsed stimulus and response signals, can be calculated after acquiring the magnitude and phase information of $v_I(t)$ from the $v_{Q1}[n]$ term.

The reception of the pulsed signal can be considered as the equivalent process in Fig. 2. First, the pulsed signal is filtered by the equivalent system frequency response $H_A(\Omega )$. The spectrum of the pulsed signal is a series of frequency components described by Eq. (4) and the filtering process introduces a linear attenuation and phase shift to $V_I(\Omega )$. The frequency spectrum of the optical pulse train is periodic pules with $1/T_s$ frequency interval, and the optical pulse sampling to the filtered signal $V_F(\Omega )$ can be translated as the convolution operation in the frequency domain. The sampled signal $V_S(\Omega )$ is the copy and shift of the filtered signal $V_F(\Omega )$ with a period of $\Omega _s=2\pi /T_s$. Through optical intensity digitization, the spectrum of the first Nyquist region can be obtained from the digital signal $V_{Q1}(\omega )$, containing the magnitude and phase information of all frequency components in $V_I(\omega )$.

The equivalent system frequency response $H_A(\Omega )$ in Fig. 2 can be derived as the Fourier transform of $h_A(t)$. According to the theoretical derivation in [15], when the OID bandwidth is more than half of the optical pulse repetition rate, the equivalent system frequency response can be written as

(7)$$H_A(\Omega) ={-}0.5\frac{R}{T_s}H_M(\Omega)P_S(\Omega),$$

where $P_S(\Omega )$ is the corresponding Fourier transform of $p_s(t)$, and $H_M(\Omega)$ is the frequency response of the MZM. Currently, commercial MZM bandwidth has reached 110 GHz and numerous mode-locked lasers are capable of generating ultrashort optical pulses, providing considerable bandwidth [16,17]. Therefore, the system bandwidth is sufficient enough to capture the abundant frequency components in $V_I(\Omega )$ when the pulse width of the pulsed signal is lower than ns level. Since the optical sampling of the pulsed signal is asynchronous and the broad spectrum of the pulsed signal is obtained, the reception method adopted by the proposed p-MPVNA is called asynchronous wideband detection. Theoretically, the asynchronous wideband detection method can also be implemented by other technologies besides microwave photonic ones.

With a low sampling rate, $1/T_s$, the frequency components in the pulsed signal are aliased to the first Nyquist zone. In the DSP module, the aliased frequencies are calculated as [15,18]

(8)$$\omega ^{'}_{k} =\left \{ \begin{array}{l} (i+1)\pi-\omega_k, i = odd\\ \omega_k-i\pi, i = even \end{array} \right.,$$

where $\omega _{k}=\omega _0+2\pi k/T_p$ represents the $k$th sideband frequency before aliasing, $i=\left \lfloor \omega _k/\pi \right \rfloor$, and $\left \lfloor \cdot \right \rfloor$ represents the floor function. The phase reverse caused by the frequency aliasing is also corrected in DSP, and the digital spectrum of the pulsed signal is recovered. Since the pulse energy is concentrated in the main lobe, the magnitude and phase of the frequency components in the main lobe are acquired sequentially, as the $V_{Q1}(\omega )$ signal with multiple sidebands shown in Fig. 2. The recovered digital spectrum in the main lobe is

(9)$$V_{Q1}(\omega) = \frac{2\pi^2 \tau A T_s}{T_p}H_A(\omega)\sum_{k={-}m}^{m}{\rm sinc}(\frac{\pi k\tau}{T_p})e^{j(\phi-\omega_0\frac{\triangle t}{T_p}-2\pi k \frac{\triangle t}{T_p})}\delta(\omega-\omega_0-\frac{2\pi k}{T_p}),$$

where $\omega =\Omega T_s$ is the digital angular frequency, and $m=\left \lfloor T_p/\tau \right \rfloor$. The number of spectral lines in the main lobe is $2m+1$, inversely proportional to the duty cycle of the pulsed signal. Consider that the system frequency response is flat within the main lobe frequency band, the $\pm k$th sidebands have the same magnitude, and the phases are symmetric to the phase at central frequency. The phase of each frequency component consists of three terms $(\phi -\omega _0\frac {\triangle t}{T_p}-2\pi k \frac {\triangle t}{T_p})$. For all frequency components, the first and second terms are common and the third term is different and also related to $\triangle t$. When $\triangle t=0.5T_p$, the odd sidebands have an opposite phase with that of the central frequency, and the vector superposition is diminished. When the starting timing of the pulsed signal is at the midpoint of the pulse envelope, i.e. $\triangle t=0$, the sidebands have the same phase as the central frequency, which means the optimal timing to start sampling is the midpoint of the pulse envelope. In this case, the vector superposition of the sidebands within main lobe is

(10)$$S = 2\pi^2 AT_s\varepsilon\sum_{k={-}m}^{m}{\rm sinc}(k\pi\varepsilon)e^{j\phi},$$

where $\varepsilon =\tau /T_p$ represents the pulse duty cycle. As shown in Fig. 3, when the duty cycle $\varepsilon$ is reduced, the magnitude of the vector superposition result $\left |S\right |$ tends to be a constant denoted as $C$.

Fig. 3. The variation of the vector superposition magnitude with the pulse duty cycle.

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Assuming that the system noise is white with power density $N_0$, the noises in these sidebands are also vector superimposed $2m+1$ times. The noise power after vector superposition should be

(11)$$N = (2m+1)N_0 = (2\left\lfloor1/\varepsilon\right\rfloor+1)N_0,$$

Therefore, the dynamic range of the proposed asynchronous wideband detection using vector superposition can be estimated as

(12)$${\rm DR_{AWD}} = \frac{C}{N_0}\cdot\frac{1}{2\left\lfloor1/\varepsilon\right\rfloor+1}.$$

Since $C$ and $N_0$ are constant independent of the duty cycle, the dynamic range decreases as 10log[1/(2$\times$floor(1/duty cycle)+1)], approximate to $\sim$10log(duty cycle) when pulse duty cycle is below 10$\%$.

Narrowband detection employed in the conventional pulsed VNA only utilizes the central frequency component to acquire the magnitude and phase of the pulsed signal. The magnitude of the central frequency component, $2\pi ^2A\varepsilon$, is proportional to the pulse duty cycle, and the dynamic range of narrowband detection is

(13)$${\rm DR_{ND}} = \frac{4\pi^4A^2\varepsilon^2}{N_0},$$

which decreases as 20log(duty cycle) [8,19].

The ${\rm DR_{AWD}}$ and the ${\rm DR_{ND}}$ decrease curves are depicted in the Fig. 4. It can be seen that when the pulse duty cycle reduces lower than 70$\%$, the asynchronous wideband detection with the vector superposition decreases slower than that of the narrowband detection. Both detection methods have a high dynamic range with a higher duty cycle. However, the proposed p-MPVNA shows an improved dynamic range in the low duty cycle situation, which is expected in some application scenarios [3].

Fig. 4. The dynamic range decrease of the narrowband detection and the asynchronous wideband detection with vector superposition method.

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3. Experiment setup and results

To verify the theoretical analysis and system performance, we established a p-MPVNA experimentally, shown in Fig. 5. As a typical application of the p-MPVNA, a 6$\sim$18 GHz microwave amplifier is employed as the DUT1 to conduct pulsed S-parameter measurements. The signal generator for DUT1 test is composed of a 100 kHz to 43.5 GHz microwave source (Rohde & Schwarz, SMF 100A), and a pulse generator. The single tone signal from the microwave source is directly sent to the test set and then stimulates the DUT1 while the periodic pulse train from the pulse generator is utilized to control the power supply of the DUT1. With pulsed power supply, the DUT1 operates periodically and the output of the DUT1 is a pulsed single tone signal in sync with the pulsed power supply. The test set consists of a single pole double throw switch (SPDTS), two power splitters (PSs), and two directional couplers (DCs), all of which have a bandwidth of over 40 GHz. SPDTS can toggle the pulsed stimulation signal to one of the DUT ports. The two PSs are used to separate the reference and incident signals from the SPDTS output and DCs can send the response signals to the ODSR. In the optical direct sampling receiver, an optical pulse train with a 250 MHz repetition rate is generated from a mode locked laser (MLL) and divided into four channels. In each channel, a 40 Gbps Mach-Zehnder modulator (MZM) and an OID is applied. Since the OID consists of a 2 GHz photodiode (PD) and a 2 GHz analog to digital convertor (ADC), the bandwidth of the OID is over half of the 250 MHz optical pulse repetition rate. The optical pulse train samples the pulsed RF signal through the quadrature-biased MZM, and are converted into the electrical pulses by the PD. The ADC is synchronized with the optical pulse train to sample and quantize at the peak of the electrical pulses. In synchronization path, a fraction of optical pulse train is converted to electrical pulses, and sent to a phase lock loop after filtering and amplification. The output signal is adopted as the sampling clock of the ADC. The sampling start timing is set to the midpoint of the pulse envelope to ensure maximum dynamic range. The digital signals are sent to the DSP to calculate the pulsed S-parameters with vector superposition.

Fig. 5. The experimental p-MPVNA for microwave amplifier and low pass filter measurement. MG: Microwave generator; PG: Pulse generator; SPSTS: Single pole single throw switch; SPDTS: Single pole double throw switch; PS: Power splitter; DC: Directional coupler; MLL: Mode locked laser; OC: Optical coupler; MZM: Mach-Zehnder modulator; PD: Photodiode; ADC: Analog to digital convertor; SYN: Synchronization; DSP: Digital signal processing; DUT1: Microwave amplifier; DUT2: Low pass filter.

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In the measurement of DUT1, the applied pulse width is 500 ns and the pulse period varies with the duty cycle. The signal power from MG is −35 dBm so that the amplifier can operate linearly. As shown in Fig. 6(a), (c) and (e), the gain curve of the microwave amplifier varies with the power supply. In continuous power supply, the gain of the microwave amplifier under test is $\sim$32 dB. With 20$\%$ duty cycle pulsed power supply, the gain increased by $\sim$3 dB, and with 5$\%$ duty cycle pulsed power supply, the gain curve is significantly changed. Continuous power supply keeps the amplifier operating, which can produce self-heating and trapping effects. Pulsed power supply allows the amplifier to return to the initial state when the pulse is off, altering the operating state of the amplifier. Fig. 6(b), (d) and (f) show the corresponding phase shifts of the microwave amplifier with different power supplies. These results are consistent with those of the commercial VNA (R&S ZNA43) with narrowband detection.

Fig. 6. The measured gain and phase shift of the microwave amplifier with different pulsed power supply. (a) and (b), continuous; (c) and (d), 20$\%$ duty cycle; (e) and (f), 5$\%$ duty cycle.

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Since the passive devices have the consistent response under the pulsed stimulation and the continuous one, a low pass filter with 10 GHz bandwidth is employed as the DUT2 to validate the dynamic range decrease with duty cycle under pulsed stimulation. The experimental setup is also demonstrated in Fig. 5. The signal generator for DUT2 test is composed of a microwave source, a pulse generator, and a single pole single throw switch (SPSTS). The single tone from the microwave generator is modulated by the periodic pulse train from the pulse generator through the SPSTS, and sent to the test set. In DSP module, the central frequency of the digital signal is captured to perform a narrowband detection, and the frequency components in the main lobe are vector superimposed to perform the proposed asynchronous wideband detection.

In the test, the widths of the pulsed stimulation are set to 400 ns and the duty cycles are set to 1$\%$ and 10$\%$, respectively. 100 pulses of 1$\%$ duty cycle and 1000 pulses of 10$\%$ duty cycle are captured for a single frequency point. Fig. 7(a) shows the S21 magnitude of the low pass filter measured with continuous and pulsed stimulation. Under continuous stimulation, the dynamic range of the p-MPVNA is $\sim$70 dB. Under pulsed stimulation, the pulsed S-parameters are obtained thru narrowband detection and the asynchronous wideband detection, respectively. When applying the narrowband detection, the dynamic range for 10$\%$ duty cycle is $\sim$50.3 dB, while the dynamic range for 1$\%$ duty cycle decreases to $\sim$31.3 dB. When applying the asynchronous wideband detection, the dynamic range of 10$\%$ duty cycle is $\sim$57.4 dB and the dynamic range of 1$\%$ duty cycle is $\sim$48.4 dB. Fig. 7(b) illustrates the relative dynamic range decrease of two detection methods at 10$\%$ and 1$\%$ duty cycle, compared with the results with continuous stimulation. The experimental results are basically matched with the theoretical calculations, indicating that the proposed p-MPVNA with asynchronous wideband detection effectively makes the system dynamic range decrease at a rate of $\sim$10log(duty cycle). Fig. 8 shows the corresponding S21 phase responses of the filter with different stimulations and detection methods, which is aligned with the measured magnitude response. The magnitude and phase response measured by a commercial VNA (Anritsu MS46522B) is provided as a reference.

Fig. 7. (a)The S21 magnitude of the low pass filter measured with continuous and pulsed stimulation. (b) The dynamic range decrease with duty cycle.

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Fig. 8. The S21 phase of the low pass filter measured with continuous and pulsed stimulation.

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4. Conclusion

We propose a p-MPVNA based on direct sampling for pulsed S-parameter measurement. Pulsed measurement employs pulsed stimulation or pulsed power supply to make the device under test produce pulsed response signals. The broad system bandwidth and undersampling technique enable the p-MPVNA to adopt an asynchronous wideband detection and vector superposition method for pulsed S-parameter measurement. The asynchronous wideband detection discretizes the continuous spectrum of the pulsed signal into abundant frequency components, and the optical pulse train in ODSR with a low repetition rate undersamples the pulsed signal to alias the frequency components. By digital signal processing, the frequency components in the main lobe are collected and recovered to calculate the pulsed S-parameters with vector superposition method. Utilizing the majority of the pulse signal energy concentrated in the main lobe, the system dynamic range decreases as $\sim$10log(duty cycle) when pulse duty cycle is below 10$\%$, which is much slower than the decrease rate of narrowband detection. We establish an experimental p-MPVNA to validate the principle and analysis. A microwave amplifier is used as the DUT with continuous and pulsed power supply. The different gain curves are obtained and compared with the result of a commercial VNA. A low-pass filter is also used as the DUT. The filter response under continuous and pulsed stimulation are measured to observe the dynamic range decrease with pulse duty cycle. The proposed p-MPVNA eliminates the minimum pulse width limitation and mitigates the desensitization phenomenon, providing a safe, reliable and effective pulsed measurement.

Funding

National Natural Science Foundation of China (61627817).

Disclosures

The authors declare no conflicts of interest to this work.

Data availability

Data underlying the results presented in this paper can be obtained from the authors upon reasonable request.

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Pulsed microwave photonic vector network analyzer based on direct sampling

Abstract

1. Introduction

2. Principle of the pulsed microwave photonic vector network analyzer

3. Experiment setup and results

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Equations (13)

Optics Express