Note: This document's copyright belongs to Paul Kiciak, N2PK, pkiciak@adelphia.net, reproduced with his permission.

The information here describes how to use a Vector Network Analyzer attached to some example components or component networks, and how to interpret the measurement results. The VNA described here is known as the N2PK VNA, but the techniques and results discussed are relevant to any VNA being used.

Any minor changes are for converting to HTML content with page jumps or splitting content, adding hyperlinks and so on - i.e. purely readability related. Any word modifications more significant than that will always be indicated in some manner (e.g. highlighting or notes), so that the original text meaning or data is not lost. This document is also under version control. All diagrams/photos are clickable to increase the resolution. If you have any corrections or comments, or some new measurement examples to share, please comment below (it is possible to insert high-res inline photos/diagrams and videos in the comments below too).

Introduction

This will be a multi-part article that describes a homebrew vector network analyzer (VNA) for transmission and reflection measurements from 0.05 to 60 MHz., with optional narrowband extensions for measurements through 500 MHz. This VNA requires an IBM compatible PC and uses custom software.

This VNA and its documentation are aimed at the serious experimenter with a basic understanding of transmission lines. An understanding of scattering (S) parameters would be helpful as well. This VNA can be replicated by anyone with moderate skills in surface mount technology.

This part describes some measurement examples. The information is useful to anyone interested in using any VNA. Later parts indicate the VNA theory of operation, a performance summary and the schematic, PCB, construction, support circuits, and acknowledgements.

Some Measurement Examples

Before describing the VNA in detail, five measurement examples are presented to give an overview of what this VNA, and VNAs in general, can do.

Series RLC Network

This example illustrates the VNA’s reflection measurement capabilities. Unlike instruments that infer the sign of the reactance (sometimes incorrectly) from impedance trends with frequency, a VNA is able to make this determination from data at a single frequency. The complex reflection coefficient is measured and then related impedance and other data are calculated.

The components are:

• 3.3 Ω,1/4 w, +/-1%, axial-leaded metal film resistor, one inch overall (lead + body) length
• 150 pF, +/-5%, 500 WVDC, mica capacitor, one inch overall (lead + body) length
• Nominal 10 uH inductor, 28 turns, #24 AWG enameled, T37-3 toroid

Lead lengths were intentionally made relatively long to demonstrate the VNA's ability to determine the associated stray inductance, predominant in these cases.

Each component was characterized independently and the series combination of all three as well. Data was collected at 100 logarithmically spaced points from 1 to 60 MHz. The measured and modeled series resistance and reactance vs. frequency results for the resistor alone are shown in Figures 1 and 2.

There is good correlation at 1 MHz between the resistance measured there and a 4-point Kelvin probe DC resistance measurement. There appears to be skin effect and proximity effect dependencies of resistance with frequency. Note however that the total change in resistance is only 130 milliohms.

Figure 2 shows good correlation of resistor reactance to an ideal 13.7 nH inductance, which is reasonable for a 1 inch long wire about 1/8 inch over a ground plane.

The measured and modeled results for the capacitor alone are shown in Figure 3. The apparent capacitance is determined assuming the stray series inductance is zero which it clearly is not. The effect of series inductance is to lower the overall measured reactance at any given frequency and hence results in an apparent capacitance that increases with frequency.

A series inductance of 17.4 nH results in a capacitance that is essentially independent of frequency, as seen in Figure 3. So a more accurate model for this component would be 147.2 pF in series with 17.4 nH. Even though the lead lengths are the same for resistor and capacitor, the resistor is closer to the ground plane and hence has lower loop inductance.

Capacitor Q would also generally be of interest. But Q exceeds 1000 in this case and such high Qs are not very reliable in this reflection measurement of the capacitor alone.

The measured and modeled results for the inductor alone are shown in Figures 4 and 5. Also shown are the real and imaginary parts of the impedance for an approximate model for the inductor consisting of a shunt combination of 14100 Ω, 10.03 uH, and 3.0 pF.

The model for the inductor is consistent with measured data over most of the 1-60 MHz range, including well above the parallel resonance at 29 MHz. Below 2 MHz, there is an increasing error in the real part of Z.

The measured results for the individual components and the series combination of all three are shown in Figures 6 and 7. Also shown is the algebraic sum of the individual component measurements, which is virtually indistinguishable from the measured series combination.

The observed series resonance is at 4.126 MHz vs. the calculated resonance at 4.135 MHz for the individually modeled components.

The series combination was ordered as LRC (capacitor grounded) to obtain the best agreement with the individual components, in particular near the inductor parallel resonance. This is judged to be primarily related to increased stray capacitance presented across the inductor near its parallel resonant frequency with alternate arrangements. More detailed models of each component would require the addition of lead to ground capacitances.

There is an almost complete absence of scatter in the measured data over nearly five orders of magnitude in R and |X|. While data scatter is only one of several elements that comprise accuracy, accuracy can certainly not be better than the scatter.

Scatter is mostly observed in Rc, which is related to the high capacitor Q. With such high Qs, reflection coefficients are near unity in magnitude. Random measurement error can cause |rho| to exceed unity in some cases with the apparent result that the component is better than lossless - one does  have to be careful when interpreting VNA measurement results!

Decoupling Capacitors

The second example is also a reflection-based measurement - of capacitors typically used for decoupling of power supply voltages near active circuits. Each capacitor was characterized independently and in various parallel combinations as well. Data was collected at 100 logarithmically spaced points from 50 kHz to 60 MHz and demonstrated the VNA’s utility below 1 MHz.

The capacitors are:

• 10 uF, 16V radial-leaded aluminum electrolytic capacitor
• Two 0.1 uF axial-leaded ceramic capacitors
• 0.01 uF ceramic disk capacitor

All components were approximately 0.45 inch overall lead plus body length.

The electrolytic capacitor was initially measured using a bridge that allowed the capacitor under test to be biased from 0 to 15V. These tests showed that the capacitor |Z| varied very little over this bias range. As a result, the data presented here was collected using a conventional return loss with the capacitors unbiased (0 VDC).

As is the convention for decoupling capacitors, the magnitude of the impedance (|Z|) is plotted here vs. frequency. However, the file data also contains the real and imaginary parts of Z, which are used as needed.

Figure 8 shows the measured |Z| for the individual capacitors. Except for Cs and Ls of the 10 uF, the following parameters can be approximately deduced from Figure 8 for each capacitor:

Due to the dominant effect on |Z| of Rs for the 10 uF capacitor over most of the plotted frequency range, the file data for Cs at 50 kHz and Ls at 60 MHz was used.

For the 0.01 and 0.1 uF capacitors, Cs is determined from |Z| at 50 kHz, Rs is the |Z| at series resonance which occurs at the respective valleys of |Z| (also 10 uF), and Ls is found by Cs and the frequency of series resonance. Alternatively, Ls can be determined from the file data based on Xs at 60 MHz; the values determined in that fashion are within 0.4 nH of the values determined from series resonance.

Next, certain two capacitor parallel combinations, selected based on broadband decoupling, were tested with the results shown on Figure 9.

As might be expected, the 10 uF in parallel with the 0.1 uF provides the better decoupling over most of the frequency range.

Last, certain three capacitor parallel combinations, also selected based on broadband decoupling, were tested with the results shown on Figure 10.

Figure 10 shows a pitfall that can occur with paralleling different value capacitors. The 10/0.1/0.01 uF combination shows first the series resonant valley at about 9.3 MHz due to the 0.1 uF, then a parallel resonant peak at about 14.3 MHz, followed by the series resonant valley at about 16.5 MHz. The extent of the actual impedance excursions is likely to be greater than shown due to the 1.2 MHz spacing between data points in this region. The parallel resonant peak primarily is the result of the series inductance of the 0.1 uF and the net  capacitive reactance of the 0.01 uF capacitor at the parallel resonant frequency.

Instead, the 10/0.1/0.1 uF combination provides better decoupling over most of the frequency range, except for a narrow window from about 15 to 30 MHz.

The two capacitor combinations in Figure 9 do not show a similar parallel resonant peak due to the relatively high Rs of the 10 uF capacitor which results in a much lower Q resonance.

Single Band Antenna Matching

The third example is also reflection based and illustrates this VNA’s ability to remotely measure impedance at high VSWR (low return loss).

The antenna is a vertical with an 11.6m overall height and a limited ground screen. There is a 2 foot piece of RG-8 coax to the antenna. PL-259PL-259 connectors are used on the antenna coax and the buried coax run back to the rig and serve as the interface to any matching units to be used. The single-band matching units for this antenna will be simple fixed component LC units, each with a pair of SO-239 connectors.

The general method used here is:

• Measure the antenna feed point impedance at a desired center frequency.
• Calculate the component values of a circuit that matches to 50 Ω coax.
• Select/build and measure the components at the center frequency.
• Check the expected match quality based on the measured components.
• Assemble the matching unit, place it at the antenna feed point, and measure input Z and VSWR.

The VNA was calibrated using homebrew PL-259PL-259 Open/Short/Load (OSL) standards located at the antenna feed point. Essentially, these calibration standards establish the VNA reference plane at the interface between the antenna coax and its PL-259PL-259 connector. The end use coax run was used for this measurement so that the VNA could remain on the bench.

A precise understanding of reference plane location is essential to perform and analyze the results of the most demanding VNA testing - even at 1.8 MHz. Also, careful construction, usage, and maintenance of calibration standards is essential to obtain the best possible VNA accuracy.

At 1.82 MHz, the measured Z = 7.04 - j577.2 which corresponds to a return loss of 0.018 dB, |rho| = 0.9979, and an VSWR of 953:1 - a challenge indeed to match in a low loss fashion and a good test of VNA measurement accuracy!

The series L and shunt C configuration was chosen for this matcher. In this case, the C is on the rig coax side. However, with such a high Z and VSWR, stray capacitance on the antenna side also had to be accounted for. This was initially estimated to be about 5 pF.

MathCAD was used for the calculations. Component Q was also included in the calculations. Initially, inductor Q was estimated at 450 based on Amidon data for the T200-2 core and a capacitance Q of 1000 was assumed.

The results of the MathCAD calculations are:

• L = 50.458 uH
• C = 4040 pF
• Total loss = 0.74 dB

The inductor was initially constructed on the T200-2 core, but was found to have minor variations in inductance with power level from 50 mW to 100 watts and it also dissipated excessive power. As a result, a pair of inductors, close-wound on PVC forms, was used instead. The VNA measured L=50.1 uH and Q=250 for the pair in series. In this case, Q was measured with a 150 pF mica capacitor in series resonance, as a shunt impedance in a two port network to obtain better accuracy.

The capacitance is formed with eight 510 pF micas. The stray capacitance, due to the connectors on the antenna side of the matching unit, was measured at 4.4 pF. Since the inductor is now physically larger, the original estimate of 5 pF was increased to 6 pF.

Here’s a picture of the 160m matching unit:

Since there were some differences between the desired or estimated and the measured values, the MathCAD program was used to re-check the match using the measured and new estimated values. The predicted match was still good with VSWR=1.13 and return loss=24 dB at 1.82 MHz.

The results of the antenna with the above matching unit, at 1 kHz steps, are shown in Figures 11 and 12.

Clearly, a good impedance match has been obtained, quite close to the 1.82 MHz design point, without resorting to intentionally adjustable components. The 2:1 VSWR bandwidth is relatively low at about 18 kHz, which is typical for such relatively short antennas. Changing the spacing between turns on the larger inductor can also be used to move the minimum VSWR point to make this unit usable over the lower 40 kHz of this band which covers the author’s interest here.

9 MHz FM Crystal Filter

A three-crystal noise filter was desired for a homebrew FM VHF receiver to filter broadband noise generated in the early IF stages. All components to be used in this filter are fixed value - no adjustable components were planned. The desired bandwidth is 15 kHz and the filter input and output impedances are 50 Ω.

First, the primary crystal parameters, determining series and parallel resonance, were calculated using the VNA measured data:

The series resonant frequencies were within 370 Hz for these three units. In the interest of brevity, not all significant digits needed to accurately represent the series resonant frequency are shown above. Also not discussed are many details that are required to accurately characterize crystals.

A trial filter design was done in simulation and using Wes Hayward's software as a general guide. The transformers, for use in a 50 Ω environment, and other parts were measured using the VNA and the PSpice simulation model was refined using the new component parameters. The filter was constructed and measured for insertion loss and group delay vs. frequency.

There was some lack of correlation between measured and simulated results. This was found, in part, due to minor measurement problems where a pi model was needed for some components and not originally included. It was also estimated that the undesired close-in crystal spurious responses might be having a measurable reduction on filter bandwidth. So, the spurious crystal responses were then measured and their parameters were generated and included in the simulation model. Once that and the other component model changes were done, the simulation model came into very close agreement with measured data. From there, minor changes to two components were made using the simulation model and confirmed in a filter test to obtain a slightly wider bandwidth and equalized group delay distortion (GDD) at the ends of the filter pass band.

Here’s a picture of the filter in its tested form:

To achieve the desired bandwidth, which is relatively wide for a ladder crystal filter, balanced transformers with neutralization capacitors are used on the end sections and a neutralization inductor is used in the middle section.

Here’s a summary of measured and simulated filter parameters:

In addition to the tabular data, the correlations between measured and simulated filter responses are also shown vs. frequency (250 Hz steps) in Figures 13 and 14.

The correlation between measured and simulated insertion loss is quite good, even including the responses at the crystal spurs between 9.035 and 9.040 MHz.

Not shown here is the good correlation near the crystal spurs at 9.085 and 9.113 MHz with insertion loss peaks at 19 and 41 dB respectively. In actual usage, these spurious peaks will require that this filter be preceded by a higher order filter that will hopefully reduce the combined spurious responses to an acceptable level.

Group delay is typically of interest only around the filter nose and is plotted here over a narrower frequency range. As with insertion loss, the correlation in group delay is quite good. Group delay, which requires accurate measurement of small phase changes with frequency, is the more difficult of the two parameters to obtain accurately.

The correlation between measured and simulated filter data also demonstrates how the VNA data is internally consistent between its reflection and transmission measurement modes. This is the result of taking reflection based component data, putting that data into a simulation model that predicts filter transmission characteristics that, in turn, match VNA measured transmission data to a high degree.

F_t for a PN2222 Transistor

This last measurement example demonstrates full two port measurement of S-parameters on a non-linear device.

F_t is a measure of the gain-bandwidth product of the transistor. It is normally determined by the product of |beta| and the test frequency. That product is approximately constant when the test frequency places |beta| on the roll-off portion of its curve.

The transistor was configured as common emitter and biased thru a pair of 100 uH inductors - each 43 turns on a FT37-61 core. The inductors have a self-resonant frequency of about 20 MHz, which was desirable to minimize their effect on measured data. Inductor saturation was checked and was not found to be a problem up to 40 mA.

The VNA directly measures the two-port S-parameters, which are then converted to H-parameters. Measured F_t is the product of |H₂₁| and the test frequency.

VNA calibrations were done at the transistor connection points using a piece of braid for the short, a 49.9 Ω chip resistor for the load, and a short wire jumper for the thru. Each port was left open for the open calibration load. The low frequency drive was reduced to about -42 dBm for S₁₁ and S₂₁ to maintain small-signal conditions.

Here’s the measured and simulated results for a PN2222 at Vce=10 V and Ic=10 mA:

Both measured and simulated results support the expected 6 dB/octave roll-off of |beta| with frequency.

In addition, data was collected at Ic=5, 2, 1, and 0.5 mA. Figure 15 shows the comparison of measured and simulated Ft vs. collector current at a test frequency of 40 MHz. Also shown are Motorola data for the similar MPS2222 at Vce=20 V.

The correlation between the measured and the Motorola data is particularly striking. Normally there's a peak in Ft, but apparently the collector currents used weren't high enough for that to occur. The Motorola datasheet indicates that peak occurs at Ic=25 mA in this transistor.

Summary

This document covered some example measurement scenarios with a Vector Network Analyzer (VNA). It was shown how a VNA can be used for measuring passive components at different frequencies. An example antenna matching scenario was also shown. A high-end crystal filter was developed using the VNA, and the gain-bandwidth product of a transistor was measured too.

To learn more about the VNA, check out HF Vector Network Analyzer - Theory of Operation