# Part II: Antenna Parameters and Measurements

Part I of this two-article series discussed the antenna models and the construction details of the half-wave dipole, quarter-wave monopole, log-periodic, and biconical antenna. Part II focuses on the log-periodic and biconical antenna impedance, VSWR, and the radiated emissions measurements.

## Antenna Impedance and VSWR

Consider the transmission line circuit shown in Figure 1. A sinusoidal voltage source S with its source impedance S drives a lossless transmission line with characteristic impedance ZC, terminated in a reactive load L. Figure 1: Transmission line circuit driven by a sinusoidal source

For an arbitrary reactive load, the magnitudes of voltage and current along the line at any distance d away from the load vary sinusoidally , as shown in Figure 2. Figure 2: Magnitudes of the voltage and current for an arbitrary load

For any value of the load, except for the matched load, the magnitudes of the voltage and current vary along the line. This variation is quantitatively described by the voltage standing wave ratio (VSWR) defined as (1)

VSWR can also be expressed in terms of the magnitude of the load reflection coefficient as (2)

where the load reflection coefficient is obtained from (3)

When the load is matched, i.e., L = ZC the load reflection coefficient, L = 0, and VSWR = 1. In this case, the magnitudes of the voltage and current along the line are constant, as shown in Figure 3. Figure 3: Magnitudes of the voltage and current for a matched load

Now, consider the model of an antenna system in the receiving mode shown in Figure 4. Figure 4: Antenna in the receiving mode

Spectrum analyzer is matched to the coaxial cable (thus, there are no reflections at the receiver). If the antenna’s radiation resistance were 50 Ω over the measurement frequency range then the voltage induced at the base of the antenna would appear at the spectrum analyzer (assuming no cable loss). If the antenna’s resistance differed from 50 Ω then some of the power received by the antenna would be reflected back or reradiated and the reading at the spectrum analyzer would be lower.

It is therefore very useful to know the impedance of the antenna over its measurement range. One very good indicator of the antenna impedance is obtained by measuring its impedance or VSWR (s11 measurements) of the antenna with a network analyzer, as shown in Figure 5, where the antenna circuit model consists of the radiation resistance Rrad and its reactance Xant. Figure 5: Antenna model

If, in a given frequency range the antenna’s impedance is purely resistive and equals 50 Ω then the VSWR reading will be 1. The more the impedance of the antenna differs from 50 Ω the higher the VSWR reading.

## Antenna Impedance and VSWR Measurements

Figure 6 shows the details of the VNA setup up and the VNA calibration prior to taking the measurements. Figure 6: VNA setup and calibration

A calibration of the network analyzer was performed inside the semi anechoic chamber at the end of the cable that connects to the antenna using short, open and load calibration standards. This is shown in Figure 6 where a calibration standard (gold in color) is connected to the cable. The calibration was performed with the cable positioned as close as possible to the final antenna-measurement configuration.

The impedance and VSWR measurements for the log-periodic antenna were performed with the antenna in both the horizontal and vertical orientation (polarization), as shown in Figure 7. Figure 7: Log-periodic antenna polarization

Figure 8 shows the impedance and VSWR for the log-periodic antenna in a horizontal polarization, while Figure 9 shows the results for the vertical polarization. Figure 8: Impedance and VSWR for log-periodic antenna in horizontal polarization Figure 9: Impedance and VSWR for log-periodic antenna in vertical polarization

The impedance and VSWR measurements for the bicon antenna were performed with the antenna in both the horizontal and vertical orientation, as shown in Figure 10. Figure 10: Bicon antenna polarization

Figure 11 shows the impedance and VSWR for the log-periodic antenna in a horizontal polarization, while Figure 12 shows the results for the vertical polarization. Figure 11: Impedance and VSWR for bicon antenna in horizontal polarization Figure 12: Impedance and VSWR for bicon antenna in vertical polarization

The measurement setup inside the semi-anechoic chamber for the radiated emissions measurements (according to CISPR25) using a biconical antenna is shown in Figures 13 and 14, . Figure 13: Measurement setup using a biconical antenna (top view) Figure 14: Measurement setup using a biconnical antenna (side view)

The wave radiating from the equipment under test (EUT) is captured by the measuring antenna connected through a coax cable to the receiver (spectrum analyzer or EMI receiver).

The voltage measured by this receiver is rec. In order to relate this voltage reading to the actual electric field measured by the antenna, Êinc we need the so-called antenna factor (supplied by the antenna manufacturer).

Antenna factor is defined as (4)

That is, the antenna factor is the ratio of the incident electric field at the measurement antenna to the received voltage at the antenna terminal. Antenna factor is usually given in dB: (5)

It is provided by the antenna manufacturer either as a table or a plot vs. frequency. From Eq. (5) we get (6)

In order to account for the cable loss we need to modify the above equation to (7)

The biconnical antenna measurement results (horizontal polarization) are shown in Figure 15. Figure 15: Biconnical antenna measurements results

The log-periodic antenna measurement results (horizontal polarization) are shown in Figure 16. Figure 16: Log-periodic antenna measurements results

## References

1. Bogdan Adamczyk, “Dipole-Type Antennas in EMC Testing – Part I: Antenna Models and Construction,” In Compliance Magazine, June 2020.
2. Bogdan Adamczyk, Foundations of Electromagnetic Compatibility with Practical Applications,
Wiley, 2017.
3. Bogdan Adamczyk, “Standing Waves on Transmission Lines and VSWR Measurements,” In Compliance Magazine, November 2017.
4. Bogdan Adamczyk, “Radiated Emissions Measurements – OATS and ALSE Methods,” In Compliance Magazine, December 2017.