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.

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].

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

Resistor impedance curves are shown in Figure 4.

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

(1)

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) |
C_{par} (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 6 shows the measurement setup used to obtain the impedance curves for three different capacitor values.

Capacitor impedance curves are shown in Figure 7.

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

Inductor impedance curves are shown in Figure 10.

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) |
C_{par} (pF) |

22 | 2174 | 0.244 |

100 | 943.27 | 0.285 |

220 | 611.8 | 0.308 |

#### Table 3: Inductor – parasitic capacitance

**References**

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