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Non-Contact Measurement Method for High Frequency Impedance of Load at the End of Wire Harness.


Corresponding to the recent shift to electric vehicles, the increase of internet usage and the evolution of driving support functions, on-vehicle electronics are increasing. For vehicles emphasizing safety and reliance, EMC design robustness is important and forced to be strengthened more and more in the future.

Regarding the EMC performance of a vehicle, not only noise sources or victim devices but also the wire harness connected to these devices need to be considered. Any noise from the noise source can radiate through the connector and onto the wire harness which acts as an antenna and radiates the noise to the inside and outside of the vehicle. When outside noise is induced on the wire harness, it can flow into the device through the connector and cause a malfunction of on-vehicle electronics.

For these reasons, the load impedance of the circuit connected to the wire harness is critical in determining the values of the EMI filter taking emission and immunity into consideration and the accurate estimation is treated as important [1]-[3]

In conventional research, a non-contact measurement method of the load impedance was previously proposed [4]. However it was confirmed only up to 30 MHz. There are many radio equipment installed in the vehicle operating at a frequency above 30 MHz, such as FM and GPS receivers.

In this study, we first tried to expand the applicable frequency to 100 MHz, the frequency band for FM receivers. Specifically, we represented the wire harness by a distributed constant circuit and, proposed to expand the non-contact impedance measurement method to the high frequency using transmission line theory. We then verified the results experimentally.

In section 2 of this study, we introduced a conventional non-contact impedance measurement method. In section 3, we expanded the applicable frequency of the non-contact measurement method to the high frequency by applying transmission line theory to the wire harness and proposed a method to estimate the characteristic impedance and phase constant of the wire harness. In section 4, we verified the experiment to validate proposed method. This paper concludes in section 5.


2.1. Summary of Non-Contact Measurement Method

Figure 1 shows a non-contact measurement setup for the impedance of a load [Z.sub.L] connected to an end of a wire. The measurement setup consists of an injection current probe, a receiving current probe and a vector network analyzer. The injection current probe was connected to Port 1 of the network analyzer and generated an AC current into the closed loop of the wire. The receiving probe was connected to Port 2 and was used to measure the current.

Figure 2 shows an equivalent circuit of the measurement system. In this figure, [L.sub.1] and [L.sub.2] are the inductances of the injection current probe and the receiving current probe, respectively. [V.sub.p1] is the signal source voltage of Port 1 and [V.sub.p2] is the received voltage at Port2. [Z.sub.p1] and [Z.sub.p2] are the input impedances of the two probes, respectively. [L.sub.w] and [r.sub.w] are the inductance and resistance of the wire. [M.sub.1] and [M.sub.2] are the mutual inductances between the wire and, the injection and receiving current probes, respectively. [I.sub.w] is the current flowing through the closed loop of the wire. For the equivalent circuit in Figure 2, the Equation can be described as follows:

[mathematical expression not reproducible] (1)

By rearranging Equation (1) to eliminate I1 and I2, the load impedance [Z.sub.L] was determined as follows:

[Z.sub.L] = K (p1/p.2) - [Z.sub.setup] (2)

where, K and [Z.sub.setup] are the calibration factors that represent the characteristics of the measurement system and are functions of [M.sub.1], [M.sub.2], [Z.sub.p1], [Z.sub.p2], [L.sub.w] [r.sub.w] and the transfer impedance [Z.sub.T2] of the receiving current probe. Next, using [S.sub.11] and [S.sub.21] measured with the network analyzer, it was possible to determine the voltage ratio [V.sub.p1]/[V.sub.p2] using the following Equation.

p1/p2 = [S.sub.11] + 1/[S.sub.21] (3)

In addition, the calibration factors K and [Z.sub.setup] were determined using the following steps prior to the measurements:

* Measured [S.sub.11] and [S.sub.21] using the network analyzer with the ends of the closed loop connected to a 0fi resistor and determined the voltage ratio [V.sub.p1]/[V.sub.p2] using Equation (3).

* Measured [S.sub.11] and [S.sub.21] using the network analyzer with the ends of the closed loop connected to a known calibration resistor [] and determined the voltage ratio [V.sub.p1]/[V.sub.p2] using Equation (3).

* Calculated the calibration factors K and [Z.sub.setup] that represent the characteristics of the measurement system by using the following Equations:

[mathematical expression not reproducible] (4)

[mathematical expression not reproducible] (5)

When the calibration factors K and [Z.sub.setup] were determined for the measurement system, it was possible to determine the impedance of an unknown load connected to an end of a wire by measuring [S.sub.11] and [S.sub.21] and substituting them into Equations (2) and (3).

2.2. Problem of Non-Contact Measurement Method

With wires whose lengths are electrically short with respect to wavelength, we worked to confirm the influence on the measurement result.

For the non-contact measurement method, we focused on the load connected to a wire. In this case, the wire can be treated as a transmission line. The load impedance on the wire as seen by the current probe is determined as follows [5]:

[] = [Z.sub.0] [Z.sub.L]+[jZ.sub.0] tan([beta]d)/[Z.sub.0]+[jZ.sub.L] tan([beta]d) (6)

where [Z.sub.0] and [beta] are the characteristic impedance and the phase constant of the transmission line, respectively. d is the wire length between the measurement point and the load.

The circuit simulation model developed to quantify the influence of the transmission line is shown in Figure 3. The S-parameters of the loop which includes the transmission line (RLCG in Figure 3) and the load (R1 in Figure 3) can be obtained by the two RF ports (P1 and P2 in Figure 3) .The transmission line consists of two parallel wires with a separation distance of 100 mm based on the size of current probe with a length of 150 mm which is often used for the EMC component testing in the auto industry. The theoretical transmission lines characteristic impedance is 638 D (C [approximately equal to] 5pF/m, L [approximately equal to] 213 1nH/m, [beta]/[omega] [approximately equal to] 3.4e-9) . Qucs (Quite Universal Circuit Simulator) is used for this simulation.

Figure 4 gives the simulation result. In the figure, the "Ideal" curve represents the calculated impedance given by the Equation (6) with load impedance of 319 [OMEGA], 638 [OMEGA] and 1278[OMEGA] respectively. The 150mm transmission line is sufficiently shorter electrically than its wave length at 100MHz. However, in spite of the load being resistive, the results indicate an impedance shift to either inductive or capacitive. As such, the load impedance was affected by the transmission line and, becomes difficult to measure the actual impedance of a load above 30 MHz.

On the other hand, Figure 4 for "Non-Contact" results show the calculated impedance from the simulation model of Figure 3 and like the "Ideal" results, they are also affected by the transmission line. As can be seen above in Figure 4, if the load impedance ([Z.sub.L]) is lower than the characteristic impedance ([Z.sub.o]), input impedance ([]) becomes inductive in high-frequency ranges ideally. But, all "Non-Contact" results of impedance are capacitive. Because the short circuit (R1 = 0 [OMEGA]) is used for calibration in this measurement method, the inductive impedance is corrected to zero in a calculation process. For this reason, the "Non-Contact" results are different from "Ideal".

At present, one problem associated with this method is that it is applicable only up to 30MHz.


3.1. Appling Transmission Line Theory

To extend the non-contact measurement method to higher frequencies, it is a good idea to assume a distributed line for the wire sections between the load and the current injecting and receiving probes as described in Figure 5 for the measurement system. In this system, the measured impedance is the input impedance [] including the transmission line and, not the terminal load impedance [Z.sub.L]. The results obtained by the non-contact measurement method are explained as follows:

[] = K p1/p2 -[Z.sub.setup] (7)

To derive the calibration factors K and [Z.sub.setup], it was necessary to take the portion of the transmission line into consideration. If the terminal load was a short circuit or a standard resistor [R.sub.std] the following Equations hold:

[]|[Z.sub.L]=short = K(p1/p2) [??][Z.sub.L] = short - [Z.sub.setup] (8)

[]|[Z.sub.L]=[R.sub.std] = K(p1/p2) [??][Z.sub.L] = [R.sub.std] - [Z.sub.setup] (9)

Using these Equations, the calibration factors K and [Z.sub.setup] are determined, as follows:

[mathematical expression not reproducible] (10)

[Z.sub.setup]=K p1/p2 [??][Z.sub.L] = short - []|[Z.sub.L]=short (11)

Next, the calibration factors K and [Z.sub.setup] thus determined were used to find the unknown load impedance connected to the end of the wire. By determining []|ZL=unknown from these calibration factors, Equations and subsequently substituting the result into the following Equation, it was possible to determine the unknown terminal resistance [Z.sub.L] according to the transmission line theory.

[Z.sub.L] =[]|[Z.sub.L]=inkonwn-[jZ.sub.o] tan([beta]d)/[Z.sub.0]-[]|[Z.sub.L]=unkonwn tan([beta]d) (12)

3.2. Method of Estimating Characteristic Impedance and Phase Constant

To estimate the characteristic impedance [Z.sub.0] and phase constant [beta] of the wire, and determine the calibration factors K and [Z.sub.setup], simultaneously, three terminal loads, a short circuit, [R.sub.std1], and [R.sub.std2] were used as follow:

[]|[Z.sub.L]=short = K(p1/p2) [??][Z.sub.L] = short - [Z.sub.setup] (13)

[]|[Z.sub.L]=[R.sub.std1] = K(p1/p2) [??][Z.sub.L] = [R.sub.std1] - [Z.sub.setup] (14)

[]|[Z.sub.L]=[R.sub.std2] = K(p1/p2) [??][Z.sub.L] = [R.sub.std2] - [Z.sub.setup] (15)

First, [S.sub.11] and [S.sub.21] were measured for each terminal load of short Circuit, [R.sub.std1], and [R.sub.std2] and voltage ratios [V.sub.p1]/[V.sub.p2|short],[V.sub.p1]/[V.sub.p2|Rstd1], and [V.sub.p1]/[V.sub.p2|Rstd2] were determined. Next, solutions for Kand [Z.sub.setup] were obtained from Equations (13), (14) as follows:

[mathematical expression not reproducible] (16)

[Z.sub.setup] = K p1/p2|[Z.sub.L] = short - []|[Z.sub.L= short] (17)

By incorporating Equations (16) and (17) into Equation (15), we obtain:

[mathematical expression not reproducible] 18

where, term K' was determined by the measurement. The following Equation holds on the basis of Equation (18).

K' []|[Z.sub.L]=[R.sub.std2] - []|[Z.sub.L=short]/[]|[Z.sub.L=short] - []|[Z.sub.L]=[R.sub.std1] (19)

The value on the left side of Equation (19) was determined using measurements [S.sub.11] and [S.sub.21]. The right side is expressed by using the characteristic impedance [Z.sub.0] and phase constant [beta]. [Z.sub.0] and [beta]/[omega] ([omega]: angular frequency) are frequency-independent constants. Using the least mean square method, these constants can be estimated based on the frequency characteristics of K' in the frequency band to be measured.

3.3. Measurement Procedure

The following steps summarize, the non-contact load impedance measurement method procedure proposed in this paper:

* Measure [S.sub.11] and [S.sub.21] for the following terminal loads: short circuit, [R.sub.std1], and [R.sub.std2]. Determine [V.sub.p1]/[V.sub.p2] for each terminal load using Equation (3) and calculate K' using Equation (18). In this step, for [R.sub.std1] and [R.sub.std2], use the measurements taken with the impedance analyzer as true values.

* Apply the least square method to Equation (16) to estimate the characteristic impedance of the wire [Z.sub.0] and [beta]/[omega].

* Calculate [] for the terminal loads of short circuit and [R.sub.std1] using Equation (6). Determine the calibration factors K and [Z.sub.setup] using Equations (16) and (17).

* Measure [S.sub.11] and [S.sub.21] with the terminal connected to the load [Z.sub.L] to be measured. Calculate [|ZL=unknown] using Equation (7).

* The load impedance [Z.sub.L] to be measured is obtained by Equation (12).


4.1. Experimental Condition

The validity of the measurement method proposed in this paper was empirically verified. Table 1 lists the equipment used in the verification experiment. To enhance reproducibility of the measurement, the transmission line was designed on a printed circuit board (PCB) instead of using a wire. Figure 6 shows the transmission line layout on the PCB

The transmission line is a parallel wire with a 110 mm gap, 300 mm length and 1 mm trace width. The PCB has 2 attachments to install a daughter board equipped with the load. For the measurements described in this paper, one side attachment is keeps shorted (0 fi) and the other side attachment is used to change the load.

Figure 7 shows a setup picture of the experiment. The PCB is set on polystyrene foam. An isolating cable (CANDOX 5B-002-18-18-107FBW) is used between current probe and SMA cable to suppress high frequency currents on the outside of the coaxial cable.

4.2. Measurement Result

Table 2 shows the estimated result of the characteristic impedance and phase constant of the wire. In table 2 [Z.sub.0] represents the characteristic impedance and [beta]/[omega] represents the phase constant. Calculated results are from the electromagnetic field simulator (Q3D of ANSYS). The estimated values are close to the calculated values.

Loads of 500D and 1 k[OMEGA] were measured. Figure 8 shows the measurement results. In Figure 8, the "Actual value" corresponds to the measurement of the daughter board using an impedance analyzer (E4990 of Keysight Technology).

The graphs reveal a noticeable divergence above 30 MHz between the conventional method and the "Actual value". Particularly, in the case of higher resistance, the difference is greater. The reason for this divergence is the same as what is described in Section 2.2 of this paper. In contrast, the values determined by the proposed method are very close to the "Actual value". They are within approximately a 10 % error range of the "Actual value" up to 100 MHz.

This study also examined capacitive loads. Figure 9 shows the measurement results. The capacitor has a self-resonance frequency near 75 MHz and becomes inductive at frequencies higher than 75MHz. Figure 9 shows that the proposed method closely estimates these characteristics.

Finally, this study examined inductive loads. Figure 10 shows the measurement results. The conventional method has an error in the high impedance area whereas. On the other hand, the proposed method estimates the impedance without the error.


Accurate measurement of the impedance of a load connected to a wire harness is important when designing EMI filters. However, the conventional non-contact load impedance measurement method using a network analyzer and current probes is limited at frequencies above 30 MHz, even with an error tolerance of 10%.

This paper proposed a more accurate measurement method by applying transmission line theory to the conventional method and, an estimation method for the characteristic impedance and phase constant. The proposed method was empirically verified and shown to give load impedance measurements with less than 10% error up to 100 MHz. The result is that efficient EMI filter designs can now be more easily found for the FM band.

Future works will be focused on designing EMI filters using data from the proposed method and finding ways to expand the measurement method to frequencies above 100MHz.


[1.] Garry B. and Nelson R., "Effect of impedance and frequency variation on insertion loss for a typical power line filter", Proc. IEEE EMC Symp., pp.691-695, 1998.

[2.] Zhang D., Chen D.Y., Nave M.J., and Dable D., "Measurement of noise source impedance of off-line converters", IEEE Trans. Power Electron., vol.15, no.5, pp.820-825, Sept. 2000.

[3.] See K.Y. and Deng J., "Measurement of noise source impedance of SMPS using a two probes approach", IEEE Trans. Power Electron., vol.19, no.3, pp. 8620868, May 2004.

[4.] Tarateeraseth V., Hu B., See K.Y., and Canavero F.G., "Accurate extraction of noise source impedance of an SMPS under operating condition", IEEE Trans.Power Electron., vol.25, no.1, pp.111-117, Jan. 2010.

[5.] Wadell Brian C., "Tansmission Line Design Handbook," Artech House Publishers, ISBN 0-89006-436-9, 1991

Makoto Tanaka, Yasunori Oguri, and Michihira Iida

DENSO Corporation

Chihiro Yoshikawa and Jianging Wang

Nagoya Institute of Technology

Table 1. Equipment used during experiment

Frequency range         1MHz--120MHz
Network analyzer        KeysightE5061B
Current probe           FCC F-61
Wire                    Transmission on FR-4 PCB
Calibration component   Short (0 [OMEGA]) 1608 size chip resister (*1)
                        50Q 1608 size chip resisted (*1)
                        2kQ 1608 size chip resister (*1)
Unknown load            500Q 1608 size chip resistor (*1)
                        lkQ 1608 size chip resistor (*1)
                        lOOOpF 1608 size chip capacitor (*2)
                        470nH 1608 size chip inductor ()* (3)

(*1) MCR series of Rohm (*2) MCH series of Rohm
(*3) LQW series of Murata

Table 2. Estimated and Calculated parameter of distributed line

                      Estimated   Calculated

Zo[[OMEGA]]         509         488
[beta]/[omega][s/m]   3.7e-9      5.0e-9
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Author:Tanaka, Makoto; Oguri, Yasunori; Iida, Michihira; Yoshikawa, Chihiro; Wang, Jianging
Publication:SAE International Journal of Engines
Date:Oct 1, 2017
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