A Novel Method to Acquire Circuit Transmission Characteristics by Noncontact Power Injection and Detection

I.   Introduction

As the frequency and operational rate of integrated circuits increase, and their complexity also increases. It thus becomes imperative to precisely quantify the transmission characteristics of circuits at each node within a processed printed circuit board (PCB) [1]–[4].

To accurately obtain the characteristics of a transmission line, scholars usually test it with the help of a vector network analyzer (VNA). In such a test, the PCB is connected to the VNA through a direct port connection, and characteristics such as the S-parameters of the transmission line on the PCB are acquired [5], [6]. In addition, several efforts have been made to determine the characteristics of the transmission line via time-domain reflection, in which one end of the PCB is connected to a time-domain pulse signal and the other end is connected to a standard load, and the characteristics of the transmission lines are obtained via the reflected signal [7], [8].

Although these methods can be used to test the characteristics of transmission lines, it is necessary to ensure that such test lines have connecting terminals. However, as shown in Figure 1, circuits that have already been soldered may include many interconnecting transmission lines without test terminals, and characterization using the above methods would require unacceptable disruption of the corresponding circuit structures. Therefore, the advantages of near-field measurements with noncontact circuits make this method worthy of consideration for solving the above problems [9]–[11].

Figure  1.  The traditional method of performing transmission characteristics measurement on the circuit.

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In near-field inspection methods, the radiation characteristics of a circuit are usually obtained by controlling a near-field probe to perform a near-field scan on the PCB [12], [13]. Some efforts have also used two probes for near-field measurements to verify the measurement efficiency [14], [15] and have used the measurements of one of the near-field probes as a reference to obtain more radiative characteristics of the PCB [16].

In the above processes, the near-field electric and magnetic field probes passively receive the radiation signal from the PCB. The electromagnetic radiation characteristics of the PCB must be accurately recognized. Accordingly, efforts have proposed electric and magnetic field calibration factors (CFs) [14], which are used to calculate the true electromagnetic field at the current position from the measurement results. In [17], [18] and [19], near-field broadband high-resolution electric and magnetic field probes of a PCB structure were used to measure near-field radiated signals from the PCB.

In addition, for relatively simple structures such as semirigid coaxial probes, the coupling capacitance between the probe and the PCB can be further determined based on a CF. In [20] and [21], a waveform transmitted on a signal line was obtained with the help of a coupling capacitor after near-field detection.

Furthermore, semirigid coaxial probes have been used in many works for the near-field active injection of signals into PCBs because of their higher voltage resistance characteristics than those of PCB-structured probes [22]. In [23], a near-field injection platform based on semirigid coaxial probes was designed, and injection experiments in the 1 GHz range were performed on the circuit. In [24], a 6 GHz semirigid coaxial probe was used to inject broadband signals into the PCB, and the waveform relationship between the probe input port and the PCB output port was also calculated using coupling capacitance.

In the above works, semirigid coaxial probes were mainly used for near-field signal injection, while probes of PCB structures were mainly employed for near-field detection. Furthermore, these probes were structured as passive signal measurement sensors alone or for active signal injection, which enabled the performance of near-field radiation source identification or electromagnetic immunity analyses of PCBs.

Therefore, to analyze the transmission characteristics of a circuit without destroying the circuit structure, a novel method using dual probes is proposed. In the characterization process, one probe is used for active signal injection, and the other probe is used for signal detection.

In this process, the voltage resistance and resolution of signal injection and detection must be balanced. Thus, a novel T-shaped semirigid coaxial probe is designed here. Compared with the conventional probe structure, the newly designed probe offers excellent spatial resolution while ensuring broadband characteristics.

Moreover, an equivalent circuit model is developed for characterizing the proposed method. According to the proposed model, after obtaining the response curve of the probe, the equivalent coupled circuit parameters of the probe can be calculated. Then, using the test results of the dual probes, the tested PCB transfer characteristics and the specific equivalent component parameter values are obtained. Therefore, assessing whether the performance of the test circuit satisfies a given set of application requirements is a straightforward process.

The remainder of this article is organized as follows. Section II describes the noncontact power injection and detection methods. According to the proposed method, Section III simulates and tests the performances of the proposed probe. In Section IV, the effectiveness of the proposed method is evaluated using a PCB with known parameters. In Section V, to verify the feasibility of the proposed method, the gain of the low-noise amplifier (LNA) and the transmission characteristics of the parallel microstrip lines (MLs) are measured. Finally, a summary is presented in Section VI.

II.   The Method of Noncontact Power Injection and Detection

To accurately characterize the PCB and obtain an equivalent circuit model, an overall noncontact signal injection, and detection structure is constructed, as shown in Figure 2. The injection probe couples the signal generated by the signal source into the PCB, and then the detection probe obtains the signal radiated via PCB transmission.

Figure  2.  Noncontact power injection and detection. (a) Schematic diagram of the test method. (b) Equivalent circuit structure. The green box shows the injection and detection probes. The blue box shows the coupled equivalent circuit. The brown box shows the equivalent circuit of the tested PCB.

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1   Signaling model of the proposed method

In the process as shown in Figure 2(a), the signal injected from the injection probe is denoted as ${X}\left( {\omega} \right)$, the injection and detection probes are defined as ${{H}_{{i}}\left( {\omega} \right)}$ and ${{H}_{{d}}\left( {\omega} \right)}$, the coupling between the injection probe and the test PCB is denoted as ${H}_{{p}1}\left({\omega} \right)$, the transmission characteristics of the signal in the PCB is ${H}_{{line}}\left({\omega} \right)$, the coupling between the PCB and the detection probe is ${H}_{{p}2}\left( {\omega} \right)$, and the final output is ${Y}\left( {\omega} \right)$. These relationships can be expressed as follows:

where, ${\omega}$ denotes the angular frequency, which is related to the frequency $f$ by $\omega = 2\pi \times f$.

Since the relationship between ${X}\left( {\omega} \right)$ and ${Y}\left( {\omega} \right)$ can be expressed when using VNA for testing:

Eq.(1) can be further expressed as:

The circuit equivalent model of the structure is shown in Figure 2(b). The injection and detection probes are equivalent to coaxial cables, and the impedances of these probes are $Z_1$ and $Z_2$, The coupling impedance between the signal structure of the injection probe and the reference ground is equivalent to a series connection between capacitor $C_2$ and resistor $R_1$ (the capacitor $C_4$ in series with resistor $R_2$ for the detection probe). The coupling between the injection probe and the test PCB circuit is equivalent to capacitance $C_1$ (the coupling of the detection probe is capacitance $C_3$). To solve for PCB characteristics, the components are modeled as a combination of multiple groups of inductors, resistors, and capacitors [20].

2   Equivalent modeling and parameters derivation for the proposed method

To obtain the transmission characteristics ${H}_{{line}}\left({\omega} \right)$, the remaining part of Eq.(1) needs to be solved with the input signal ${X}\left( {\omega} \right)$ and the output signal ${Y}\left( {\omega} \right)$ determined. The main focus is on the calculation of ${H}_{{p}1}\left( {\omega} \right){H}_{{i}}\left( {\omega} \right)$ and ${H}_{{p}2}\left({\omega} \right){H}_{{d}}\left( {\omega} \right)$.

The injection probe needs to couple the signal into the PCB, which is consistent with the process in [24]. As shown in Figure 3(a). The current ${i_{i}\left({\omega} \right)}$ of the signal injected into the PCB from the probe can be expressed as:

Figure  3.  Lumped model of near-field probes and PCB. (a) Model of a near-field injection probe. (b) Model of a near-field detection probe.

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where ${i_{o}\left({\omega} \right)}$ is the signal that eventually reaches the PCB. ${i_{g}\left({\omega} \right)}$ is the current at the output after the probe is coupled to the ground. Kirchhoff’s laws are used to calculate the current, and the following equation can be obtained:

Since the signal $V_{i}(\omega)$ injected by the injection probe is greater than or equal to $V_{g}(\omega)$, we consider the variable $n(\omega)$ such that ${V_{i}(\omega) = n(\omega) \times V_{g}(\omega)}$, where ${|n(\omega)| \geq 1}$. The relationship between the voltages can thus be expressed as:

As shown in Figure 3(b), the detection probe is coupled to the radiated signal of the PCB [25], [26]. The current ${i_{i1}(\omega)}$ of the signal coupled from the PCB to the probe can be expressed as:

In conjunction with the previous analysis of the injection probe, the following relationship exists when detecting the probe operation:

Since the detection signal $V_{o1}(\omega)$ output from the detection probe is less than or equal to $V_{g1}(\omega)$, we use the variable $m(\omega)$ such that ${V_{o1}(\omega) = m(\omega) \times V_{g1}(\omega)}$, where $|m(\omega)| \leq 1$. The relationship between the voltages can thus be expressed as:

For the injection probe to inject more signals into the PCB, as well as for the detection probe to couple more PCB signals, it can be seen from $H_{p1}(\omega)H_{i}(\omega)$ and $H_{p2}(\omega)H_{d}(\omega)$ given in (6) and (9) that it is necessary to ensure a coupling of large capacitances ${C_{1}}$ and ${C_{3}}$ and small capacitances ${C_{2}}$ and ${C_{4}}$.

The values of ${C_{1}}$ and ${C_{3}}$ are mainly determined by the PCB and the probe port. ${C_{2}}$ and ${C_{4}}$ are determined by the distance between the inner conductor of the probe and the ground of the outer conductor. As shown in Figure 4, the probe and the transmission line on the PCB are equated as two metal bodies, and the capacitance between them can be approximated as:

Figure  4.  Schematic diagram of the coupling capacitance model.

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where $r$ is the radius of the conductor at the probe port, $l$ is the conductor length, ${d}$ is the distance between parallel classes, and ${\varepsilon}$ and ${k}$ are the permittivity and electrostatic force constant, respectively.

III.   Designing the Required Probes and Carrying Out Characterization Tests

This section presents the design of the injection and detection probes involved in the proposed model. The characteristics of the proposed method were tested to ensure the subsequent identification of PCB characteristics.

1   Design of injection and detection probes

Considering that the near-field probes used in the proposed method need to guarantee high injection efficiency, large withstand voltages, and high sensitivity, the SR-141-M17 [27] semirigid cable is used as the base element of the probe, and the directionality of the probe is further enhanced by adding additional conductors to the output port of the center conductor.

A full-wave model of the probe is shown in Figure 5. This model includes a near-field probe, a wide bandwidth PCB circuit, and end launch connectors. Port 1 of the probe and port 2 and port 3 of the PCB are included in the whole model. The three ports in the model satisfy the following S-parameter correlation:

Figure  5.  Full-wave simulation model of the probe and the relevant parameters of the probe.

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According to (11), the S-parameter matrices of the injection and detection probes are the same. Therefore, the simulation results of the injection probe are used as the basis for the final performance of the two probes.

As shown in Figure 5, the probe comprises a semirigid cable with an outer conductor diameter of $D1 = 3.58$ mm, a dielectric diameter of $D2 = 2.99$ mm, a center conductor radius of $r = 0.46$ mm, and an added conductor with a length of $l$ and a radius of $r$.

First, the length of the semirigid cable is fixed at a constant $l1 = 20$ mm. Then, to reduce the coupling capacitance between the center conductor and the outer conductor, $l3$ is fixed to 3 mm. The probe is fixed at 0.5 mm from the PCB, the frequency range is from 100 kHz to 10 GHz, and 1001 points are selected for calculation. For the simulation optimization of probe performance, the focus is on determining the length of the dielectric layer $l2$ and the length of the added conductor $l$.

As shown in Figure 6, the whole simulation process is divided into three steps. Firstly, after determining the parameters of the probe, $S_{21}$ from port 1 to port 2 in Figure 5 is first obtained. Then, according to Figure 2(b), the equivalent circuit model is established in ADS software. Finally, the optimization algorithm of ADS software is used to acquire the equivalent $S_{21}$ curve and the corresponding circuit parameters.

Figure  6.  Process for obtaining equivalent circuit parameters of the injection and detection probes.

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As shown in Figure 7, the length of $l2$ is fixed to 0 mm, and the length of $l$ is varied from 2 mm to 14 mm. Therefore, from the first step of the simulation process, obtaining $S_{21}$ under different $l$ is available. Differences are made between $S_{21}$ at different lengths $l$ and $S_{21}$ of the structure without the additional conductor, and the results obtained are defined as the gains. As the length $l$ increases, the gain in the lower frequency band increases.

Figure  7.  Simulation results of the length $l$ of the conductor added to the probe. (a) Probe gain compared to when $l$ is 0 mm. (b) Coupling capacitance and grounding capacitance with increasing $l$.

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Above the frequency of 6 GHz, the gain becomes weaker after $l\geq8$ mm. After the third step of the simulation process is completed. The capacitance parameters at different lengths can be obtained.Since the equivalent parameters have the smallest $R_1$ and $R_2$ at ${l = 8}$ mm, the coupling capacitance almost no longer increases. Therefore the ${l}$ of the probe is selected as 8 mm by combining the above simulations.

As shown in Figure 8, the length of $l2$ is designed to vary from 0 mm to 3 mm to analyze the variation in the transmission characteristics at different lengths. The differences between $S_{21}$ of $l2$ other lengths and $S_{21}$ of $l2 = 3$ mm are defined as the gains. As the length increases, the gain difference with respect to $l2 = 3$ mm decreases. However, $C_1$ and $C_3$ remain essentially unchanged, but $C_2$ and $C_4$ slowly increase. Therefore $l2$ is determined to be 0 mm.

Figure  8.  Simulation results of the length $l2$ of the conductor added to the probe. (a) Probe gain compared to when $l2$ is 3 mm. (b) Coupling capacitance and grounding capacitance with increasing $l2$.

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2   Characteristics of the proposed method

Frequency range: As shown in Figure 9, the probe is kept parallel to the direction of the ML. Port 1 of the VNA is connected to the probe, port 2 of the VNA is connected to one end of the ML, and the other end of the ML is connected to a 50 ${\Omega}$ load. The VNA completes the measurements according to segmented settings. 201 points from 100 kHz to 20 MHz, 1001 points from 20 MHz to 100 MHz, and 1001 points from 100 MHz to 10 GHz.

Figure  9.  Measurement of the characteristics of the proposed method.

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As shown in Figure 10, the signal injection response factor $S_{21}$ (referring to the model in Figure 5) obtained from the simulation and the measurement match well. Starting at the frequency of 100 kHz, the $S_{21}$ of the probe increases rapidly, reaching −40 dB at 400MHz and −30 dB at 1.6 GHz, and then remains stable in the higher frequency range. The difference (the result of subtraction) obtained from simulation and measurement is less than 2.8 dB. These test results show that the proposed method has broadband characteristics and good stability when injecting and detecting signals.

Figure  10.  Frequency range of signal injection and detection.

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Coverage of signal injection and detection: The coverage of the method is defined as the distance of 6 dB from the maximum power position [25], [28], [29]. The radio frequency signal source SMA100B and the spectrum analyzer (SA) FSV3044 settings are consistent with the directionality of the signal injection and detection. The probe is controlled to move in the direction perpendicular to the ML (X-direction) in steps of 0.1 mm. The test results in Figure 11 fully show that the probe covers within 1.6 mm in the range of 10 GHz. Therefore, it is necessary to ensure that there are no other MLs present in the X-direction of both the injection and detection probes during noncontact signal injection and detection.

Figure  11.  Coverage of signal injection and detection.

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Suitable distance of the probes for the proposed method: The injection and detection probes are fixed at 1 mm from the ML. Port 1 of the VNA is connected to the injection probe, and port 2 is connected to the detection probe. The VNA is set to scan 1001 points at 0 dBm within 100 kHz to 10 GHz.

The distance $pd$ between the injection probe and the detection probe starts at 33 mm and approaches incrementally by 1 mm, as shown in Figure 12. As $pd$ decreases, a coupling capacitance forms between the two probes and gradually increases. When $pd$ is less than 28 mm, the capacitance becomes large enough to affect the original signal, causing resonance in the transmission curve and rendering the proposed method inoperative.

Figure  12.  Influence of change in $pd$ distance on the response of the injection probe and the detection probe.

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Influence of the height $d$ between the probe and the PCB: As shown in Figure 4, the distance $d$ between the probe and the PCB influences the coupling capacitance during signal injection and detection. Different $d$ values affect the magnitude of the injected and detected signals. The distance $pd$ is fixed at 40 mm. By adjusting $d$ from 0.5 mm to 3.5 mm in 0.5 mm steps to obtain the response curves of the injection and detection probes at different distances, the height range suitable for the proposed method is obtained.

As shown in Figure 13, as $d$ increases, the coupling capacitance between the probe and ML decreases, resulting in a weaker response between the detection and injection probe. When $d$ is greater than 2 mm, the detection probe cannot accurately acquire the injection signal. Therefore, the $d$ should be less than 2 mm during the measurement process.

Figure  13.  Influence of change in distance $d$ between probe and PCB on signal injection and detection.

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It is important to note that all the above measurements are conducted to ensure that the injection and detection probes are aligned in parallel with the ML on the PCB to achieve optimal coupling capacitance for maximum signal injection and detection efficiency.

IV.   Validation of the Feasibility of the Proposed Methodology

While validating the proposed method, it is preferable to obtain the equivalent coupling parameters of the injection probe and the detection probe. Then, the identification of the circuit characteristics can be performed by combining the relationship between the input and output signals.

1   Measurement setup

To validate the proposed method, a PCB with known circuit structure parameters is tested to determine the equivalent circuit parameters of the injection probe and the detection probe. Then, the injection and detection probes are simultaneously placed into the circuit, and the S-parameters are obtained via VNA. These results are compared with those of the equivalent circuit structure to verify the accuracy of the methodology. Therefore, the equivalent parameters of the circuit with a known structure are obtained.

2   Experimental design

To ensure a solid connection between the probe and the entire measurement system, copper foil is employed to envelop the probe, thereby guaranteeing proper alignment of the probe’s outer conductor with the reference ground of the entire system.

As shown in Figure 14, the injection probe and the detection probe were placed 0.5 mm directly above the ML, and the distance between the two probes was 35 mm. The PCB has an RO4003C substrate with a thickness of 32 mils, a width of the ML of 1.69 mm, and a height of 35 $\mu$m. The two ports of the PCB are connected using end-launch connectors with two 50 $\Omega$ loads.

Figure  14.  Schematic diagram of the measurements of the proposed method.

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Ultimately, an equivalent circuit model is created, as shown in Figure 2(b). During the model parameter determination, the VNA is set up to output signals from 100 kHz to 10 GHz with 15 dBm power and 1001 points. In step 1, the response curve of the injection probe is obtained by injecting a signal from the probe port and detecting it at the PCB port. In step 2, the response curve of the detection probe is obtained by injecting a signal from the probe port and detecting it at the PCB port. Subsequently, the equivalent parameters of the probes are obtained separately by ADS.

In step 3, as shown in Figure 14, the signal from port 1 of the VNA is injected into the circuit through the injection probe, and then the output of the detection probe is connected to port 2 of the VNA, thereby obtaining the response curve of the whole link. Then, the equivalent model of the whole link is established. The two probes with equivalent parameters and the PCB were replaced with a transmission line model. Finally, the response curve obtained from the test is used as the final optimization result to obtain the equivalent parameters of the PCB. The accuracy of the proposed method is determined by comparing it with curves obtained from the model.

3   Test results of the proposed method

As shown in Figure 15, the results obtained by equivalent circuit modeling are in good agreement with the measurements. In the model, ${Z_{1}}$ and ${Z_{2}}$ are characterized using the inductance. Therefore, the equivalent circuit parameters of the probes must be recorded in Table 1.

Figure  15.  Measurement and equivalent modeling simulation result curves for the injection and detection probes.

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Table  1.  Values of Equivalent Circuit Parameters

Component Number	Value	Component Number	Value
$Z_{1}$	1.51 nH	$C_{3}$	0.3 pF
$C_{1}$	0.28 pF	$Z_{2}$	1.3 nH
$R_{1}$	0.8 $\Omega$	$R_{l1}, R_{l2}\ldots, R_{l6}$	0.11 $\Omega$
$C_{2}$	2.1 pF	$L_{l1}, L_{l2}\ldots, L_{l6}$	0.05 nH
$R_{2}$	0.01 $\Omega$	$C_{l1}, C_{l2}\ldots, C_{l6}$	0.001 pF
$C_{4}$	0.09 pF

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The root mean square error (RMSE), as a metric for measuring the accuracy of actual data, is utilized here to characterize the differences between the proposed method and the conventional measurement approach. The formula for calculating the RMSE is as follows:

here, ${n}$ represents the number of samples, $P_{i}$ denotes the measured value of the proposed method, and $C_{i}$ represents the measurement value of the traditional method. As shown in Figure 16, based on Table 1, the S-parameters between the injection probe and the detection probe in the equivalent circuit are obtained. In addition, the actual S-parameters of both probes can be measured by the VNA test. By setting the VNA to generate high power, larger ${X}\left( {\omega} \right)$ and ${Y}\left( {\omega} \right)$ of (1) are guaranteed, which effectively prevents the signal from being too small and causes it to drown in noise. As shown in Figure 16, the maximum difference is 1.79 dB at 4 GHz, and the RMSE is 0.64 dB.

Figure  16.  S-parameter curves between the injection probe and detection probe obtained from simulation and measurement.

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The PCB with known characteristics is shown in Figure 14 is modified into an equivalent structure consisting of multiple sets of inductors, resistors, and capacitors, as shown in Figure 2(b). Combining the response curves between the injection probe and the detection probe obtained from the test, the values of each component in Table 1 can be determined (we use six groups of inductors, resistors, and capacitors for the equivalent [20]). The probes’ inherent impedances $Z_{1}$ and $Z_{2}$ are equivalent to the inductance, thus the unit henry (H) is employed.

As shown in Figure 17, comparing the transmission function of PCBs with known parameters obtained from VNA tests reveals that the equivalent model of the proposed method is consistent with the transmission loss characteristics of the actual circuit structure. For the tested PCB structures, the error between the VNA test result and the equivalent model result is less than 0.24 dB, and the RMSE is 0.14 dB.

Figure  17.  ML transmission losses obtained from direct measurements at VNA ports and equivalence of the proposed method.

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The above measurements and simulation results verify the effectiveness of the proposed method.

V.   Application of the Proposed Method

1   Measurement of amplifier response characteristics

Broadband LNAs are an integral component of many receiver devices, radar systems, and communications equipment[30]. LNAs are typically placed at the front of a system circuit for weak signal amplification or in the middle for general signal amplification. Because these circuits have been processed to differentiate the performance of the amplifier from that predicted via theory, it is necessary to test the actual performance of the amplifier (especially its gain characteristics). Corresponding and conventional test methods require the addition of test terminals at the input and output of the LNA, which destroys the circuit structure.

Therefore, in this subsection, the proposed method is used to test the gain of an LNA, and its feasibility is evaluated by comparing the results with those of a conventional direct port test.

As shown in Figure 18, the TLLA0.1G18G-30-25 LNA [31] is selected for testing. Since the LNA is sealed by the case, the ML from Figure 14 is used to connect to the port of the LNA. In this configuration, the coupling parameters of the injection and detection probes are consistent with those discussed in the previous sections.

Figure  18.  Test schematic of the response characteristics of the low noise amplifier.

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In the test, the signal at port 1 of the VNA is coupled to the ML structure through the injection probe and passed through the board to the input of the LNA. The signal is amplified by the LNA and output to the ML, which is connected to port 2 of the VNA through the detection probe. The LNA operates from 0.1 GHz to 18 GHz and has an amplification of approximately 35 dB. Therefore, in combination with the frequency range of the probe, the VNA frequency is set from 0.1 GHz to 10 GHz, the number of scanning points is 1001, and the power of the generated signal is 10 dBm. After obtaining the ${S_{21}}$ under the MLs connection only in Figure 18, the difference is made with the new ${S_{21}}$ obtained by adding the LNA to the link, and the result is the gain of the LNA.

To confirm the validity and accuracy of the measurement results of the proposed method, a direct port connection test of the LNA is performed using the VNA. Because the maximum value of the LNA input signal is -5 dBm and the maximum input signal of the VNA port is 27 dBm, the NVA frequency range is set from 0.1 GHz to 10 GHz. Testing is conducted at 1001 points with a power of -40 dBm.

In Figure 19, the LNA gain curves obtained by using the proposed method and by using the conventional method are given. The comparison reveals that the maximum error of the two methods is 1.66 dB at 0.8 GHz in the measurement band, the average overall error is 0.13 dB, the RMSE is 0.58 dB.

Figure  19.  Measurement results of the proposed method and the conventional method.

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2   Measurement of transmission characteristics of parallel corner microstrip lines

MLs are widely used in PCBs to transmit signals. With increasingly high device integration, the PCB ML spacing continues to decrease, such that multiple MLs often appear in parallel. When the distance between the MLs is too close, line coupling phenomena occur, which couples the signal originally transmitted in the ML to a similar ML. This process directly reduces the transmission quality of the signal.

A PCB with 6 MLs is used for measurement, as shown in Figure 20. The thickness of the PCB is 1.6 mm, the thickness of the MLs is 35 $\mu$m, the width of each ML is 0.762 mm, and the distance between the MLs is 0.508 mm.

Figure  20.  Test schematic for parallel MLs. The red line on the PCB represents the ML for injection and detection, and the blue MLs all have 50 $\Omega$ loads added to both ports.

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Since FR4 usually operates in the 3 GHz band and below, the frequency range of the VNA is set to 100 kHz to 3 GHz, the power is set to 10 dBm, and the number of points is set to 1001. The near-field injection probe injects the signal into the red ML at a height of 0.5 mm from the PCB, and the detection probe is located at the other end of the red ML. The 6 MLs are connected to a 50 ${\Omega}$ load at both ends.

Before testing, it is necessary to obtain the equivalent parameters of the injection and detection probes at a line width of 0.762 mm. In practical scenarios, the line widths of MLs may vary across different circuits. The necessity of fabricating each circuit and obtaining equivalent parameters through testing for different ML widths can increase the complexity of the proposed method. Therefore, we propose establishing equivalent parameter curves for various line widths of FR4 before testing, enabling direct acquisition of equivalent parameters during subsequent tests.

Therefore, a PCB with 0.2 mm, 0.3 mm, 0.4 mm, 0.5 mm, 1 mm, 2 mm, 3 mm, and 4 mm line widths is designed. As shown in Figure 21, the equivalent parameters of the injection and detection probes for different line widths are obtained by testing.

Figure  21.  Schematic of the ML injection and detection response characterization test on the FR4 substrate.

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The ${S_{21}}$ curves of the injection probe and detection probe at different line widths are tested separately using VNA, and the corresponding circuit parameters can be obtained by combining them with the equivalent circuit model in Figure 2(b) after considering the FR4 substrate. The trends of the injection probe and detection probe for different components at different line widths are shown in Figure 22.

Figure  22.  Trend curves for different parameters of the injection and detection probes. The blue curve is for the injection probe, and the brown curve is for the detection probe. (a) ${C_{1}}$ and ${C_{3}}$. (b) ${Z_{1}}$ and ${Z_{2}}$. (c) ${R_{1}}$ and ${R_{2}}$. (d) ${C_{2}}$ and ${C_{4}}$.

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After obtaining the parameters of the injection and detection probes corresponding to the 0.762 mm linewidth, further optimization is conducted in conjunction with the VNA measurements to obtain the equivalent model results shown in Figure 23. Clearly, the theoretically obtained results based on the equivalent circuit vary only slightly from the measurement results, with good agreement realized in the 3 GHz frequency band. The specific values of the parameters in the equivalent model are shown in Table 2. The probes’ inherent impedances $Z_{1}$ and $Z_{2}$ are equivalent to the inductance, thus the unit henry (H) is employed.

Figure  23.  S-parameter curves obtained from the VNA and from the equivalent model.

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Table  2.  Equivalent circuit parameters for parallel microstrip lines

Component Number	Value	Component Number	Value
$Z_{1}$	0.6 nH	$Z_{2}$	1.3 nH
$C_{1}$	0.165 pF	$R_{l1}, R_{l2}, R_{l3}$	0.1 $\Omega$
$R_{1}$	0 $\Omega$	$L_{l1}, L_{l2}, L_{l3}$	1.97 nH
$C_{2}$	1.26 pF	$C_{l1}, C_{l2}, C_{l3}$	2.27 pF
$R_{2}$	0 $\Omega$	$R_{l4}, R_{l5}, R_{l6}$	0.3 $\Omega$
$C_{4}$	1.3 pF	$L_{l4}, L_{l5}, L_{l6}$	3.79 nH
$C_{3}$	0.18 pF	$C_{l4}, C_{l5}, C_{l6}$	2.17 pF

 | Show Table

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Finally, the ML direct connection test using VNA is performed to verify the effectiveness of the proposed method. A comparison of the results obtained using the proposed method and direct VNA measurements is shown in Figure 24. The maximum error between the results obtained by the proposed method and the traditional measurement method is less than 1.47 dB in the range of 3 GHz, and the RMSE is 0.71 dB.

Figure  24.  ML transmission losses obtained from direct measurements at the VNA ports and equivalence of the proposed method.

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VI.   Conclusion

In this article, a novel method is proposed for identifying the transmission characteristics of circuits using dual probes. One probe is dedicated to signal injection, while the other is employed for signal detection. Utilizing specially designed semirigid coaxial probes featuring a T-shaped structure, the proposed method facilitates the identification of transmission characteristics within the frequency range of 10 GHz. This can be achieved with a minimum distance between the two probes exceeding 28 mm and a minimum spacing between the probes and an ML greater than 1.6 mm.

As shown in Table 3, an equivalent model corresponding to the proposed method is also proposed. The validity of the model is then confirmed through practical circuit testing. An error of less than 0.24 dB in the 10 GHz range in the ML transmission loss is achieved, and the circuit equivalent parameters are obtained based on the model.

Table  3.  Comparison of the proposed method with existing methods.

Ref.	Probe	Method	Frequency	Target	Equivalent Parameters	Max Error
[20]	E Probe	Detection	10 MHz-6 GHz	Reconstructing Signal	NO	-
[24]	E Probe	Injection	30 MHz-4 GHz	Injection Signal	NO	-
[32]	E Probe	Detection Twice	UP to 12 GHz	Transmission Characteristic	NO	17.2 dB
[2]	E probe and M probe	Detection at Two Positions	700 MHz-20 GHz	Transmission Characteristic	NO	5.2 dB
Proposed	E probe and E probe	Injection and Detection	100 kHz-10 GHz	Transmission Characteristic	YES	0.24 dB

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Finally, application tests are carried out using the proposed method for LNA gain and parallel ML circuits with FR4 as the substrate. The RMSE between the transmission characteristics obtained by the proposed method and the actual characteristics is less than 0.9 dB.

In future work, we will further verify the feasibility of the proposed method, especially in cases where the circuit impedance is unknown.

Appendix A.

For Eq. (6) can be calculated by referring to the following derivation.

Firstly, ${H_{p1}(\omega)H_{i}(\omega)}$ can be expressed as:

Subsequently, Eq. (4) can be updated by bringing back ${i_{g}(\omega)}$, ${i_{i}(\omega)}$, and ${i_{o}(\omega)}$ from Eq. (5) into Eq. (4):

The variables to be solved in the above equation are ${V_{g}(\omega)}$ and ${V_{o}(\omega)}$, which are obtained by arranging the equation:

Finally, bringing this result back to Eq. (A-1), ${H_{p1}(\omega)H_{i}(\omega)}$ can be expressed as:

Eq. (9) is also calculated by the same process as described above.

Firstly, ${H_{p2}(\omega)H_{d}(\omega)}$ can be expressed as:

Subsequently, Eq. (7) can be updated by bringing back ${i_{g1}(\omega)}$, ${i_{i1}(\omega)}$, and ${i_{o1}(\omega)}$ from Eq. (8) into Eq. (7):

The variables to be solved in the above equation are ${V_{g1}(\omega)}$ and ${V_{o1}(\omega)}$, which are obtained by arranging the equation:

Finally, bringing this result back to Eq. (A-5), ${H_{p2}(\omega)H_{d}(\omega)}$ can be expressed as: