How to determine the impedance measurement range of a network analyzer?

question

Vector network analyzers can measure impedance and Z parameters. However, in the specification manual, the impedance measurement range is rarely marked. How to determine the impedance measurement range of a network analyzer?

When you see the Z11 test result of a transmission line, can you tell its characteristic impedance?

When measuring the Z11 of an open circuit breaker, what is the curve from a few Ω to a few kΩ?

Impedance measurement range

Reflection coefficient Γ=(z-1)/(z+1), where normalized impedance z=Z/Z0

The impedance measurement range is between short circuit and open circuit, and the corresponding reflection coefficient Γ is between {-1, 1}. The reflection coefficient Γ corresponds to the single-port reflection scattering parameter S11. Usually, the reflection test accuracy is specified in the specification manual of the vector network analyzer, such as R&S ZVA: When the reflection coefficient is close to 1, the reflection measurement uncertainty is <0.015.

Assuming the reflection uncertainty range is ±0.02, the corresponding reflection coefficient range is between {-(1-0.02), (1-0.02)}.

Z=(1+Γ)/(1-Γ) *Z0

Z_max = (1+0.98)/(1-0.98)*50 = 4950Ω

Z_min = (1-0.98)/(1+0.98)*50 = 0.5Ω

RF Impedance Analysis

The RF impedance Z=R+jX, its amplitude and phase change periodically with the frequency. The following example analyzes the Z11 impedance characteristics of a transmission line + resistor.

Depending on the electrical length, the frequency response of the Z11 parameter changes periodically, and this period corresponds to twice the electrical length of the port input.

Example 1: Analysis of 5kΩ load Z11 with electrical length 100mm

Transmission line electrical length Le = 100 mm;

Transmission line impedance Zt = 50Ω;

Load resistance R = 5kΩ;

Answer: The Z11 simulation results show a 1.5GHz periodic variation.

Impedance phase zero crossing frequency: fc = C0/(2×Le) = 1.5GHz

Maximum Z11c = R = 5kΩ

Minimum value Z11p = R × (Zt/R)^2 = 0.5Ω

Example 2: Analysis of 50Ω load Z11 with electrical length 100mm

Answer: When the resistor R=5kΩ is replaced by R=50Ω, Z11=50Ω.

Example 3A: Analysis of 75Ω transmission line with electrical length of 100mm + 50Ω load Z11

Answer: When R = 50Ω, Zt = 75Ω

Impedance phase zero crossing frequency: fc = C0/(2×Le) = 1.5GHz

Peak value Z11p = R × (Zt/R)^2 = 112.5Ω

Minimum Z11c = R = 50Ω

Example 3B: Assume that the characteristic impedance of the transmission line is obtained based on the results in the above figure

Answer: Transmission line Z11t = R × SQRT(Z11p/R) = 75Ω

Example 4: Analysis of 75Ω transmission line with electrical length of 100mm + 75Ω load Z11

Answer: When R = 75Ω, Zt = 75Ω

Impedance phase zero crossing frequency: fc = C0/(2×Le) = 1.5GHz

Z11 = R = 75Ω

in conclusion

The impedance measurement range of the vector network analyzer is 0.5~4950Ω.

RF impedance varies periodically with frequency:

Impedance phase zero crossing frequency

When the impedance is matched Zt = R,

Z11 = R

The zero point of the n∙fc impedance phase is pure resistance

n∙fc/2 Impedance phase ±90° Frequency corresponding impedance

C0 = 3×10^8

The load impedance ZL at the end of the transmission line

Transmission line impedance Zt