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Estimating the Parasitics of Passive Circuit Components

This article presents a simple method of estimating the parasitics of the three passive circuit components (R, L, C). First, the non-ideal model of each component is presented, followed by the network analyzer measurements. The component (approximate) model serves as the basis for analytical calculations leading to the values of the parasitics. 

The PCB used in this study, [1], is shown in Figure 1.

Figure 1: PCB and its details

Since the calibration traces are of the same length as the traces leading to the components, the connectors and traces are effectively taken out of the measurements. Thus, the measured parasitics come from the component itself and not from the connecting traces. It should be noted that this approach is not targeting the impedance measurement accuracy but rather provides the simplest way of estimating the component parasitic values. More accurate methods exist [2-5].

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1. Resistor Model and Its Parasitics

Circuit model and the impedance vs. frequency curve (straight-line approximation) for a resistor and its parasitics (with no traces attached) are shown in Figure 2 [6,7].

Figure 2: Resistor circuit model and its impedance curve

Figure 3 shows the measurement setup used to obtain the impedance curves for three different resistor values. 

Figure 3: Measurement setup – resistor impedance curves

Resistor impedance curves are shown in Figure 4.

Figure 4: Resistor impedance curves

Each curve shows a 3-dB point corresponding the frequency (shown in Figure 1):

(1)

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From Equation 1, the parasitic capacitance can be obtained as:

(2)

The resulting parasitic capacitance values for the three resistors are shown in Table 1.

R (Ω) f (MHz) Cpar (pF)
300 1921 0.276
3000 833.5 0.064
31, 600 22.36 0.225

Table 1: Resistor – parasitic capacitance

2. Capacitor Model and Its Parasitics

Circuit model and the impedance vs. frequency curve (straight-line approximation) for a capacitor and its parasitics (with no traces attached) are shown in Figure 5 [1,2].

Figure 5: Capacitor circuit model and its impedance curve

Figure 6 shows the measurement setup used to obtain the impedance curves for three different capacitor values. 

Figure 6: Measurement setup – capacitor impedance curves

Capacitor impedance curves are shown in Figure 7.

Figure 7: Capacitor impedance curves

Each curve shows a self-resonant point corresponding the frequency (shown in Figure 5):

 (3)

From Equation 3 the parasitic inductance can be obtained as:

 (4)

The resulting parasitic inductance values for the three capacitors are shown in Table 2.

C (nF) f (MHz) Lpar (nH)
1 463.1 0.12
10 66.0 0.58
100 21.4 0.55

Table 2: Capacitor – parasitic inductance

3. Inductor Model and Its Parasitics

Circuit model and the impedance vs. frequency curve (straight-line approximation) for an inductor and its parasitics (with no traces attached) are shown in Figure 8 [1,2].

Figure 8: Inductor circuit model and its impedance curve

Figure 9 shows the measurement setup used to obtain the impedance curves for three different inductor values. 

Figure 9: Measurement setup – inductor impedance curves

Inductor impedance curves are shown in Figure 10.

Figure 10: Inductor impedance curves

Each curve shows a self-resonant point corresponding the frequency (shown in Figure 9):

 (5)

From Equation 3 the parasitic inductance can be obtained as:

 (6)

The resulting parasitic capacitance values for the three inductors are shown in Table 3. 

L (nH) f (MHz) Cpar (pF)
22 2174 0.244
100 943.27 0.285
220 611.8 0.308

Table 3: Inductor – parasitic capacitance

References

  1. Haring, D., designer of the PCB used in this study
  2. https://www.mwrf.com/technologies/test-measurement/article/21849791/copper-mountain-technologies-make-accurate-impedance-measurements-using-a-vna
  3. https://www.clarke.com.au/pdf/CMT_Accurate_Measurements_VNA.pdf
  4. https://passive-components.eu/accurately-measure-ceramic-capacitors-by-extending-vna-range
  5. https://www.w0qe.com/Measuring_High_Z_with_VNA.html
  6. Adamczyk, B., Teune, J., “Impedance of the Four Passive Circuit Components: R, L, C, and a PCB Trace,” In Compliance Magazine, January 2019.
  7. Adamczyk, B., “Basic Bode Plots in EMC Applications – Part II – Examples”, In Compliance Magazine, May 2019.

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