Photonic-assisted fast broadband microwave vector network analyzer based on FMCW

Chen Xiaoen; Wang Long; Ding Min; Chen Jianping; Wu Guiling

doi:10.1364/OE.506110

1. Introduction

Vector network analyzer (VNA) is a crucial instrument in various scenarios, such as charactering microwave devices, tumor detection, and so on [1–4]. So far, the maximum bandwidth of the commercial VNAs without dedicated external frequency converters is 67 GHz, which are based on the solutions of frequency sweeping and microwave mixing [4–6]. But these two solutions face the challenge of measurement speed, linearity and spuriousness in a wide frequency range, respectively. For a broadband measurement, such as 0.1-40 GHz, the measurement speeds of commercial VNAs are at the level of several seconds, which will even increase to tens of seconds with the increase of the number of frequency sweeping points [7]. It cannot meet the demand for fast broadband signal measurement, which is increasing with the rapid development of information technology [8]. For instance, monitoring of sudden changes is essential for analysis of signals evolution process, and failure causes in broadband circuits design [9,10]. Also, monitoring vital sign in medical and health settings needs wide bandwidth and fast speed to achieve low resolution and real-time measurement, respectively, such as a bandwidth of 30 GHz and measurement time of 166.26 ns [11]. Therefore, it is important to improve the measurement speed and bandwidth of VNAs.

To speed up measurement and overcome the electronic bottleneck, several microwave photonic VNAs have been proposed in recent years. Frankel et al. demonstrated an ultrahigh-bandwidth VNA based on equivalent time electro-optic sample technique [12], which is achieved through varying optical delay rail. The bandwidth of 100 GHz and measurement time of 10 $\mathrm{\mu}$s are achieved. A single-shot network analyzer (SiNA) based on photonic time stretch and impulse response measurement was proposed to obtain the frequency response of a Mach-Zehnder modulator (MZM) and a photodetector (PD) [13,14]. A bandwidth of 40 GHz and a measurement time of 27 ns were achieved. However, the two schemes have a limited frequency resolution by the repetition frequency of mode-locked lasers (MLL). A broadband frequency response measurement scheme based on stimulated Brillouin scattering and frequency conversion is proposed in [15]. A bandwidth of 66.8 GHz is achieved using a 40-Gbps dual-drive Mach-Zehnder modulator. Optoelectronic vector analyzers through coherent receivers [16] or up- and down-conversions [17] are also realized. However, these schemes require the electrical backend with bandwidth equal to the measurement frequency range, which limits reachable bandwidth and increases the cost. Its measurement time lengthens with the increase of the number of frequency sweeping points. We have proposed wideband VNAs based on direct microwave photonic digitization [18,19] and photonic harmonic mixing [20] in previous work. The bandwidth of 40 GHz is achieved using an electrical backend with narrow bandwidth. The measurement time, however, still lengthens with the number of frequency sweeping points. A concept of photonic based on THz heterodyne phase-coherent techniques is proposed [21]. To date, however, no experimental validation is reported. In [22], a pulsed free space two-port photonic VNA with up to 2 THz bandwidth was experimentally demonstrated. It, however, cannot cover the measurement within tens of GHz or lower frequency band, since the photomixers used in scheme can only work in the range roughly from 0.1 THz to 4 THz [23].

This paper presents a photonic-assisted fast broadband microwave VNA (FB-VNA) based on FMCW. An electrical FMCW is carrier-suppressed single-sideband (CS-SSB) modulated on the continuous wave (CW) light. The bandwidth of the generated optical FMCW is extended by a recirculating frequency shift (RFS) loop. The bandwidth-extended optical FMCW beats with the CW light to generate the broadband electrical FMCW, which serves as the incident signal of the device under test (DUT). The response signals of the DUT (transmission signal and reflection signal) are modulated on the bandwidth-extended optical FMCW to achieve de-chirping, respectively. By coherently beating the modulated light with the CW light, the response signals of the DUT are down-converted to single-tone intermediate frequency (IF) signals. The IF signal is captured by an analog-to-digital converter (ADC), and the S parameters of the DUT can be obtained from the amplitude and phase of the IF signal after Hilbert transform. A reference channel is added to eliminate the influence of the system response. 41-times bandwidth multiplication from 6-18 GHz to 6-498 GHz is experimentally demonstrated. With available device, a 6-54 GHz FB-VNA is demonstrated, and the S parameters of a 25-GHz low-pass filter (LPF) is measured within 6 $\mathrm{\mu}$s. The sudden changes of ${S_{21}}$ parameter of DUT are also characterized by the proposed FB-VNA, which is simulated by fast adjusting the bias voltage of the MZM used for de-chirping. The sudden changes as short as 0.01 $\mathrm{\mu}$s can be captured.

2. Principle

The schematic of the proposed FB-VNA is shown in Fig. 1. A CW light is first CS-SSB modulated by an electrical FMCW to generate the optical FMCW. The optical FMCW is launched into the RFS loop to extend the bandwidth, which consists of a dual-parallel MZM (DP-MZM) to achieve frequency shift by CS-SSB modulation, an erbium-doped fiber amplifier (EDFA) to compensate for the loss of the RFS loop, an optical bandpass filter (OBPF2) to adjust the frequency shifter times, and a delay fiber to make the time delay of the RFS loop match the FMCW pulse width. So that the adjacent FMCW pulses can be spliced without delay and no reduction to the efficient bandwidth of each FMCW pulse is brought by the de-chirping operation.

Fig. 1. Schematic of FB-VNA. OC: Optical coupler. MZM: Mach-Zehnder modulator. AWG: Arbitrary waveform generator OBPF: Optical bandpass filter. EDFA: Erbium-doped fiber amplifier. PC: Polarization controller. DP-MZM: Dual-parallel MZM. PD: Photodetector. LNA: Low-noise amplifier. PWD: Power divider. MS: Microwave switch. DC: Directional coupler. DUT: Device under test. OTDL: Optical tunable delay line. BPD: Balanced PD. DSP: Digital signal processing.

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Generally, the optical field of the optical FMCW output from the RFS loop can be expressed as

(1)$${E_{{\textrm{O} - \textrm{FMCW}}}}\left( t \right) = {a_{{\textrm{O} - \textrm{FMCW}}}}\exp \left[ {j\left( {{\omega _o}t + \pi \gamma {t^2}} \right)} \right],0 \le t \le T,$$

where ${a_{{\textrm{O} - \textrm{FMCW}}}}$ is the complex amplitude, ${\omega _o}$ is the initial angular frequency, $\gamma$ and $T$ are the chirp rate and the period of the optical FMCW. The incident signal of the DUT generated by beating the optical FMCW with CW light can be expressed as

(2)$$\ {V_{{\textrm{E} -\textrm{FMCW}}}}\left( t \right) = {a_{{\textrm{E} -\textrm{FMCW}}}}\cos \left( {{\omega _e}t + \pi \gamma {t^2}} \right),$$

where ${a_{{\textrm{E} -\textrm{FMCW}}}}$ is the amplitude of the incident signal which is related to ${a_{{\textrm{O} -\textrm{FMCW}}}}$, the complex amplitude of CW light, the responsivity of the PD and etc., ${\omega _e} = {\omega _o} - {\omega _c}$ is the initial frequency of the incident signal, ${\omega _c}$ is the optical frequency of the CW light.

In the signal separation module, the power divider (PWD) is used to separate the reference signal and incident signal of DUT, the microwave switch (MS) is used to choose the incident port of DUT (port-a or port-b, $a = 1,2$, $b = 1,2$), and the directional couplers (DCs) are used to separate the transmission and reflection signals.

Taking one test channel as an example, when the MS is switched to port ②, the response signal of DUT can be written as [24]

(3)$${V_{{\textrm{DUT}}}}\left( t \right) = {a_{{\textrm{E} -\textrm{FMCW}}}}\left| {{S_{ab}}\left( {{\omega _d}\left( t \right)} \right)} \right|\cos \left( {{\omega _e}\left( {t - {\tau _1}} \right) + \pi \gamma {{\left( {t - {\tau _1}} \right)}^2} + \angle {S_{ab}}\left( {{\omega _d}\left( t \right)} \right)} \right),$$

where $\left | {{S_{ab}}\left ( \omega \right )} \right |$ and $\angle {S_{ab}}\left ( \omega \right )$ are the magnitude and phase of the S parameters of DUT at the frequency $\omega$ from port-b to port-a, ${\omega _d}\left ( t \right )$ is the instantaneous frequency of the FMCW, ${\tau _1}$ is the time delay of the path from PD to the RF input port of MZM3, and ${\tau _1} \le t \le T + {\tau _1}$. The optical FMCW ${E_{{\textrm{O} -\textrm{FMCW}}}}\left ( t \right )$ is launched into MZM3 after a time delay ${\tau _2}$. Under the condition of small signal, the output optical field of MZM3 can be express as

(4)$$\begin{aligned} {E_{{\textrm{MZM}}}}\left( t \right) = & {E_{{\textrm{O} -\textrm{FMCW}}}}\left( {t - {\tau _2}} \right) \times \cos \left( {\frac{{\pi \left[ {{V_b}\left( t \right) + {V_{{\textrm{DUT}}}}\left( t \right)} \right]}}{{2{V_\pi }}}} \right)\\ \approx & {E_{{\textrm{O} -\textrm{FMCW}}}}\left( {t - {\tau _2}} \right) \times \left[ {\cos \frac{{\pi {V_b}\left( t \right)}}{{2{V_\pi }}} - \frac{\pi }{{2{V_\pi }}}\sin \frac{{\pi {V_b}\left( t \right)}}{{2{V_\pi }}} \times {V_{{\textrm{DUT}}}}\left( t \right)} \right]\\ = & {a_{{\textrm{O} -\textrm{FMCW}}}}\cos \frac{{\pi {V_b}\left( t \right)}}{{2{V_\pi }}} \times \exp \left\{ {j\left[ {{\omega _o}\left( {t - {\tau _2}} \right) + \pi \gamma {{\left( {t - {\tau _2}} \right)}^2}} \right]} \right\}\\ & - \frac{{\pi {a_{{\textrm{O} -\textrm{FMCW}}}}{a_{{\textrm{E} -\textrm{FMCW}}}}}}{{4{V_\pi }}}\left| {{S_{ab}}\left( {{\omega _d}\left( t \right)} \right)} \right|\sin \frac{{\pi {V_b}\left( t \right)}}{{2{V_\pi }}}\\ & \times \exp \left\{ {j\left[ {\left( {{\omega _o} + {\omega _e}} \right)t + 2\pi \gamma {{\left( {t - \frac{{{\tau _1} + {\tau _2}}}{2}} \right)}^2} + \angle {S_{ab}}\left( {{\omega _d}\left( t \right)} \right) + {C_1}} \right]} \right\}\\ & - \frac{{\pi {a_{{\textrm{O} -\textrm{FMCW}}}}{a_{{\textrm{E} -\textrm{FMCW}}}}}}{{4{V_\pi }}}\left| {{S_{ab}}\left( {{\omega _d}\left( t \right)} \right)} \right|\sin \frac{{\pi {V_b}\left( t \right)}}{{2{V_\pi }}}\\ & \times \exp \left\{ {j\left[ {{\omega _c}t + 2\pi \gamma \left( {{\tau _1} - {\tau _2}} \right)t - \angle {S_{ab}}\left( {{\omega _d}\left( t \right)} \right) + {C_2}} \right]} \right\}, \end{aligned}$$

where ${V_b}\left ( t \right )$ is the bias voltage of MZM3, ${C_1}$ and ${C_2}$ are constants. It can be seen from Eq. (4) that the first term is a FMCW with an instantaneous frequency of ${\omega _o} + 2\pi \gamma t$, the second term is also a FMCW with an instantaneous frequency of ${\omega _o} + {\omega _e} + 4\pi \gamma t$, and the third term is a single-tone signal with a frequency of ${\omega _c} + 2\pi \gamma \left ( {{\tau _1} - {\tau _2}} \right )$. After coherently beating ${E_{{\textrm{MZM}}}}\left ( t \right )$ with the CW light at the balanced photodetectors (BPDs), the first two terms will be down-converted to the electrical FMCWs. An analog or digital bandpass filter (BPF) after BPDs can be used to filter out these two FMCWs with high start frequency. The direct currents introduced by the nonideal BPDs will be filter out, either. And the third term of Eq. (4) will be down-converted to an electrical single-tone IF signal with a frequency of $2\pi \gamma \left ( {{\tau _1} - {\tau _2}} \right )$. After neglecting the first and second terms of Eq. (4), the output signal of BPD is exactly the IF signal, ${V_{{\textrm{IF} -\textrm{test}}}}\left ( t \right )$, which can be written as

(5)$$\begin{aligned} {V_{{\textrm{IF} -\textrm{test}}}}\left( t \right) \approx & 2\left( {{\eta _1} + {\eta _2}} \right){\textrm{Re}}\left[ {j{E_{{\textrm{MZM}}}}\left( t \right)E_{{\textrm{CW}}}^*\left( t \right)} \right]\\ \approx & - \frac{{\pi \left( {{\eta _1} + {\eta _2}} \right){a_o}{a_{{\textrm{O} -\textrm{FMCW}}}}{a_{{\textrm{E} -\textrm{FMCW}}}}}}{{2{V_\pi }}}\left| {{S_{ab}}\left( {{\omega _d}\left( t \right)} \right)} \right|\sin \frac{{\pi {V_b}\left( t \right)}}{{2{V_\pi }}}\\ & \times \cos \left( {2\pi \gamma \left( {{\tau _1} - {\tau _2}} \right)t - \angle {S_{ab}}\left( {{\omega _d}\left( t \right)} \right) + {C_2}} \right), \end{aligned}$$

where ${\eta _1}$ and ${\eta _2}$ are the responsivity of the two PDs in BPD. The amplitude- and phase-frequency responses of DUT are contained in the IF signal, and can be extracted by Hilbert transform. In the same way, the IF signal in the reference channel can be written as

(6)$$\ \begin{aligned} {V_{{\textrm{IF} -\textrm{ref}}}}\left( t \right) = & - \frac{{\pi \left( {{\eta _1} + {\eta _2}} \right){a_o}{a_{{\textrm{O} -\textrm{FMCW}}}}{a_{{\textrm{E} -\textrm{FMCW}}}}}}{{2{V_\pi }}}\sin \frac{{\pi {V_b}'}}{{2{V_\pi }}}\\ & \times \cos \left( {2\pi \gamma \left( {{\tau _1}' - {\tau _2}'} \right)t + {C_2}'} \right) \end{aligned}$$

where ${\tau _1}'$ and ${\tau _2}'$ are the corresponding time delays in the reference channel, respectively, ${V_b}'$ is the bias voltage of MZM2 and set as ${V_\pi }$ to maximize ${V_{{\textrm{IF} -\textrm{ref}}}}\left ( t \right )$. It is worth noting that the other parameters are assumed to be the same in the three channels, considering that they can be calibrated via standard calibration kits [25]. Additionally, the differences between ${\tau _1} - {\tau _2}$ and ${\tau _1}' - {\tau _2}'$ can be eliminated by finely adjusting the time delay, ${\tau _1}$ and ${\tau _1}'$, through the optical tunable delay lines (OTDLs) placed before the MZMs. At this time, the calibration technique of commercial VNAs can be implemented for the proposed VNA. The differences between ${\tau _1} - {\tau _2}$ and ${\tau _1}' - {\tau _2}'$ can be evaluated from the frequency differences of IF signals in the test and reference channels. Thus, the S parameters can be obtained by

(7)$$\begin{aligned} {S_{ab}}\left( {{\omega _d}} \right)\sin \frac{{\pi {V_b}\left( t \right)}}{{2{V_\pi }}} = & \frac{{{V_{{\textrm{IF} -\textrm{test}}}}\left( t \right) + j{{\hat V}_{{\textrm{IF} -\textrm{test}}}}\left( t \right)}}{{{V_{{\textrm{IF} -\textrm{ref}}}}\left( t \right) + j{{\hat V}_{{\textrm{IF} -\textrm{ref}}}}\left( t \right)}}\\ = & \left| {{S_{ab}}\left( {{\omega _d}\left( t \right)} \right)} \right|\sin \frac{{\pi {V_b}\left( t \right)}}{{2{V_\pi }}} \times \exp \left\{ {j\left[ { - \angle {S_{ab}}\left( {{\omega _d}\left( t \right)} \right) + C} \right]} \right\} \end{aligned}$$

where $C$ is a constant, ${\hat V_{{\textrm{IF} -\textrm{test}}}}\left ( t \right )$ and ${\hat V_{{\textrm{IF} -\textrm{ref}}}}\left ( t \right )$ are the Hilbert transform of ${V_{{\textrm{IF} -\textrm{test}}}}\left ( t \right )$ and ${V_{{\textrm{IF} -\textrm{ref}}}}\left ( t \right )$, respectively. It can be seen from Eq. (7) that when ${V_b}\left ( t \right )$ is set as ${V_\pi }$, the accurate S parameters can be obtained.

3. Experiments and results

3.1 Generation of broadband FMCW

A laser (PPCL300) with a wavelength of 1550.2 nm and linewidth of 10 kHz is used as the CW light source, which is then divided into three paths by optical coupler 1 (OC1). One of the outputs of OC1 is launched into a 40-Gbps MZM1 (Fujitsu, FTM7939EK) biased at null point to maximize the power of the optical FMCW. An arbitrary waveform generator (AWG, Keysight, M8195A) with a sampling rate of 65 GSa/s is used to generate electrical FMCW with a start frequency, stop frequency, pulse width, and period of 6 GHz, 18 GHz, 1.25 $\mathrm{\mu}$s, and 50 $\mathrm{\mu}$s, respectively, corresponding to a chirp rate of $\gamma = 9.6{\,\textrm{GHz}/\mathrm{\mu}\textrm{s}}$. OBPF1 (Finisar, WaveShaper 16000S) with the center wavelength of 1550.1 nm and bandwidth of 0.1 nm is used to filter out the +1st sideband to achieve the CS-SSB modulation. The measured output optical spectrums of MZM1 and OBPF1 are shown in Fig. 2 (a). It can be seen that the power ratio of +1st sideband to carrier and other sideband can reach 25 dB and more than 41 dB, respectively.

Fig. 2. (a) Output optical spectrums of MZM1 (blue curve) and OBPF1 (red curve). (b) Input (blue curve) and output (red curve) optical spectrums of RFS loop. The insert shows the input (blue curve) and output (red curve) optical spectrums of DP-MZM when the center wavelength and bandwidth of OBPF2 are set as 1547.5 nm and 4 nm.

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The output of OBPF1 is launched into the RFS loop, which consists of a polarization controller (PC), a DP-MZM (iXblue, MXIQ-LN-30), an EDFA, an OBPF2 (Santec, OTF-970), and a 200-m delay fiber. The two RF inputs of the DP-MZM are orthogonal single-tone signals with frequency of 12 GHz from a 90-degree hybrid, whose input signal is from the AWG. The center wavelength and bandwidth of OBPF2 are set as 1547.5 nm and 4 nm, respectively. The 200-m delay fiber introduces a time delay of about 1 $\mathrm{\mu}$s. Adding the time delay of other devices in the RFS loop, the total time delay of the RFS loop is about 1.25 $\mathrm{\mu}$s. Therefore, by setting the pulse width of FMCW to 1.25 $\mathrm{\mu}$s, breakpoints between adjacent FMCW pulses are avoided. The input and output spectrums of the RFS loop is shown in Fig. 2 (b). 41-times bandwidth multiplication from 6-18 GHz (0.096 nm) to 6-498 GHz (3.936 nm) with a flatness within 3 dB is achieved. The insert in Fig. 2 (b) shows the input (blue curve) and output (red curve) optical spectrums of DP-MZM. The ratio of the power of +1st sideband to that of the carrier and other order sidebands reaches 23 dB.

3.2 Measurement of S parameters

The above generation of broadband FMCW based on RFS loop promise the potential of a proposed VNA system with a bandwidth of 6-498 GHz as long as the bandwidths of PDs and MZMs can reach the same value [26]. With the available 50-GHz PD (U2T, XPDV21x0(RA)) and 40-Gbps MZMs in our lab, the proposed FB-VNA with a bandwidth of 6-54 GHz is demonstrated. The center wavelength and bandwidth of OBPF2 are set as 1549.95 nm and 0.4 nm. As shown in Fig. 3 (a), 4-times bandwidth multiplication from 6-18 GHz (0.096 nm) to 6-54 GHz (0.384 nm) with a flatness within 3 dB is achieved. The spectrum of the generated broadband electrical FMCW after a low-noise amplifier (LNA, SHF S807C) is shown as Fig. 3 (b).

The BPDs have the bandwidth of 200 MHz, and the ADC has a bandwidth of 650 MHz and sampling rate of ${f_s} = 1.6{\,\textrm{GSa/s}}$. By finely adjusting the OTDL in each channel, the IF signal in each channel has a similar frequency of about 80 MHz, which is within the bandwidth of electrical backend.

Fig. 3. (a) Input (blue curve) and output (red curve) optical spectrums of the RFS loop when the center wavelength and bandwidth of OBPF2 are set as 1549.95 nm and 0.4 nm. (b) Spectrum of the broadband electrical FMCW.

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Since the proposed VNA is based on time-domain signal processing, its frequency resolution is determined by the chirp rate of FMCW, $\gamma$ and the sampling rate of the ADC, ${f_s}$, as

(8)$$\delta f = \gamma /{f_s}.$$

The ADC has a sampling rate of 1.6 GSa/s, achieving a frequency resolution of 6 MHz for $\gamma = 9.6{\,\textrm{GHz}/\mathrm{\mu}\textrm{s}}$. For broadband DUTs, this frequency resolution is enough for most of applications. For narrow-band DUTs, FMCW with lower chirp rate and ADCs with higher sampling rate can be used to lower the frequency resolution.

A LPF with the bandwidth of 25 GHz serves as the DUT. The measured four pairs of S parameters by the proposed VNA and a commercial VNA (Anritsu Shockline, MS46522B) are shown in Fig. 4. The maximum frequency of MS46522B is 43.5 GHz. The two measurement results are both calibrated using standard calibration kits (Keysight, 85056D) through the Short-Open-Load-Through (SOLT) method [25]. A 3-dB bandwidth of 25 GHz can be seen from ${S_{21}}$ and ${S_{12}}$. There are protrusions around 25 GHz and oscillation within 33-40 GHz in the magnitude of ${S_{21}}$ and ${S_{12}}$, which is caused by the circuit of LPF, itself. The S parameters within 40-54 GHz are suspect, since the 3-dB bandwidths of PWD and DCs are 40 GHz. The PWD and DCs with broader bandwidth have been reported in [27,28], which can be employed to broaden bandwidth. The S parameters from 54 GHz to the end are also suspect because there are no signals within 5 $\mathrm{\mu}$s to 6 $\mathrm{\mu}$s of each period. More times of frequency shift can be set to cover this frequency range. The deviations between the two results are shown at the right axis of Fig. 4. The mean and standard variance of $\left | {{S_{21}}} \right |$ deviation in the passband are 0.3398 dB and 0.2434 dB, respectively. The low deviations validate that the S parameters measured by the proposed VNA are accurate and reliable. The obvious gaps within 25-33 GHz and 40-43.5 GHz are caused by the dynamic range (DR) difference between the two VNAs and the bandwidth limitation of the PWD and DCs, respectively. From Fig. 4 (b), DRs of the proposed VNA and MS46522B can be read as about 30 dB (IF bandwidth: 20 MHz) and 50 dB (IF bandwidth: 500 kHz), respectively. Narrowing the IF bandwidth can reduce noise power and improve DR. In the experiment, a 20-MHz digital BPF is adopted as the IF filter. Considering the order of digital IF filters is proportional to the ratio of sampling rate to the bandwidth, it is hard to achieve an IF bandwidth narrower than 20 MHz at the sampling rate of 1.6 GSa/s. An analog BPF with narrower bandwidth can be adopted to improve DR, but is not available in hand.

Fig. 4. Measured S parameters of a 25-GHz LPF and the deviation between this work and the commercial VNA (MS46522B). (a)-(d) Magnitude of ${S_{11}}$, ${S_{12}}$, ${S_{21}}$, ${S_{22}}$, and the deviation. (e)–(h) Unwrapped phase of ${S_{11}}$, ${S_{12}}$, ${S_{21}}$, ${S_{22}}$, and deviation.

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The upper limit of DR of the proposed VNA is determined by the maximum IF power, which is related to the attenuation of the system and maximum input FMCW power. The system has different attenuation for different input frequency. Generally, as the input frequency increases, the attenuation also increases. With reported [26] or commercial broadband MZM, the increasing of attenuation can be lessened. The maximum input FMCW power is related to the 0.1-dB compression point of MZM and the power of the generated FMCW. Figure 3 (b) indicates that the power of the generated FMCW has not reached the compression point of MZM (measured as about 15 dBm). The power of the generated FMCW can be improved by utilizing the broadband high-power PD [29] and amplifier [30]. The lower limit of DR is decided by the minimum detectable IF amplitude in the time domain, which is mainly influenced by the time-domain noise floor and the least significant bit (LSB) of ADC. The time-domain noise floor is mainly contributed by the thermal noise, shot noise, and amplifier spontaneous emission (ASE) noise. Since these noise can be considered as white, the amplitude of the time-domain noise floor, ${a_{{\textrm{noise}}}}$ can be considered as three times the noise standard deviation, according to the three-sigma guideline. It can be written as

(9)$${a_{{\textrm{noise}}}} \approx 3{\sigma _0} = 3\sqrt {{B_{{\textrm{IF}}}}{N_0}} ,$$

where ${\sigma _0}$ is the standard deviation of the noise, ${B_{{\textrm{IF}}}}$ is the IF bandwidth, ${N_0}$ is the power spectral density (PSD) of the noise. Thus, the noise floor can be suppressed by decreasing the IF bandwidth. The decreasing of ${B_{{\textrm{IF}}}}$ can be achieved by adjusting the bandwidth of the analog or digital BPF after the BPD. While ${B_{{\textrm{IF}}}}$ is reduced by a factor of $m$, the DR increases by a factor of $10\lg \left ( m \right )$ in decibel unit. As ${a_{{\textrm{noise}}}}$ decreases to the level lower than the LSB, ADC with higher digitalizing bit can be used to further improve DR. It is reasonable since ADC with high digitalizing bit but narrow bandwidth is easy to implement. As for the DR of the commercial VNA [31], the upper limit is the highest input power level, that is usually determined by the compression specification of the receiver. The lower limit is decided by the noise floor, which is mainly introduced by thermal noise and has a power of

(10)$${P_{{\textrm{th}}}} = k{T_0}{B_{{\textrm{IF}}}},$$

where $k$ is Boltzmann constant, ${T_0}$ is absolute temperature. Also, when ${B_{{\textrm{IF}}}}$ is reduced by a factor of $m$, the DR increases by a factor of $10\lg \left ( m \right )$ in decibel unit.

3.3 Monitoring of sudden changes

Owe to the fast measurement speed, the proposed scheme is capable of monitoring sudden changes related to S parameters. Since a fast time-varied DUT is not available at hand, the bias voltage of MZM in one test channel is fast adjusted to simulate the time-variation of S parameters. It is reasonable. According to Eq. (7), when ${V_b}\left ( t \right )$ is time-varied, the measured ${S_{21}}$ can be considered as the product of ${S_{21}}\left ( {{\omega _d}\left ( t \right )} \right )$ and $\sin \left [ {\pi {V_b}\left ( t \right )/2{V_\pi }} \right ]$, As shown in Fig. 5, the time-varied bias voltage can be equivalent to a virtual DUT (V-DUT) with ${S_{21}}$ of $\sin \left [ {\pi {V_b}\left ( t \right )/2{V_\pi }} \right ]$, while the bias voltage of MZM is set as ${V_\pi }$. The equivalent DUT (E-DUT) is the cascade of the DUT and V-DUT.

Fig. 5. Scheme of the equivalent relation between the time varying bias voltage and the time varying S parameters. (a) Actual scheme in which the bias voltage of MZM is time-varied. (b) Equivalent scheme in which the time-varied bias voltage is equivalent to a virtual DUT (V-DUT).

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In the experiment, a 0.5-m microwave coaxial cable serves as the DUT, MS is switched to port ② and the bias voltage of MZM3 is controlled by an AFG (Rigol, DG5102) to generate sudden changes. The bias voltage applied on MZM3 is shown as Fig. 6 (a). Within the time window of 40 $\mathrm{\mu}$s, there are five sudden changes, 1.75 V within 1 $\mathrm{\mu}$s, 2.5 V within 0.01 $\mathrm{\mu}$s, 0.75 V within 2 $\mathrm{\mu}$s, 1 V within 8 $\mathrm{\mu}$s and 1.75 V within 1us. The measured ${S_{21}}$s of the E-DUT are shown in Fig. 6 (b). At the beginning and end of the time window of 40 $\mathrm{\mu}$s, there are two ${S_{21}}$s of incomplete frequency band, and they are not plotted. Six complete ${S_{21}}$s are measured within 40 $\mathrm{\mu}$s. The protrusion at the end of each ${S_{21}}$ is because there are no signals from 54 GHz to the end. It can be seen that the first four sudden changes are completely captured, whose the sudden times are measured with the error lower than 0.04 $\mathrm{\mu}$s, which are mainly derived from the time jitter of the ADC, the noise and the bandwidth limitation of the bias voltage input port of MZM. The results indicate that the proposed scheme is able to capture the sudden changes of DUT as short as 0.01 $\mathrm{\mu}$s.

Fig. 6. (a) Time-varied bias voltage of MZM3 with five sudden changes. (b) Measured six complete ${S_{21}}$ with sudden changes captured.

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4. Conclusion

In conclusion, we propose and demonstrate a photonic-assisted FB-VNA based on FMCW, whose measurable frequency range is largely extended by the RFS loop and measurement speed is accelerated by using FMCW as the incident signal. By controlling the OBPF in the RFS loop, 41-times bandwidth multiplication from 6-18 GHz (0.096 nm) to 6-498 GHz (3.936 nm) is achieved. With broadband PD and MZMs, the measurable frequency range of the proposed VNA can reach 6-498 GHz. With the available PD and MZM, a 6-54 GHz FB-VNA is demonstrated, and the S parameters of a 25-GHz LPF is measured within 6 $\mathrm{\mu}$s. Its ability to capture the sudden changes of DUTs is also validated by measuring the sudden changes simulated by fast changing the bias voltage of MZM used for de-chirping. The results indicate that the proposed scheme is able to capture the sudden changes of DUT as short as 0.01 $\mathrm{\mu}$s.

Funding

National Natural Science Foundation of China (61627817).

Disclosures

The authors declare no conflicts of interest.

Data availability

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.

References

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Photonic-assisted fast broadband microwave vector network analyzer based on FMCW

Abstract

1. Introduction

2. Principle

3. Experiments and results

3.1 Generation of broadband FMCW

3.2 Measurement of S parameters

3.3 Monitoring of sudden changes

4. Conclusion

Funding

Disclosures

Data availability

References

Data availability

Cited By

Figures (6)

Equations (10)

Optics Express