Vector Network Analysis (VNA) has become a powerful tool in the shack of many amateurs. To get the best out of one of these useful instruments it’s important to be familiar with a method of graphical representation known as a Smith Chart. We will start by explaining how the Smith Chart works before moving on to showing how a VNA can be used to perform some basic tasks. 

The Smith Chart

Used in conjunction with VNA, a Smith Chart is an extremely valuable tool that helps you visualise the behaviour of an antenna and the arrangements for feeding and matching it to a transmitter. Figure 2 shows the basic arrangement of a Smith Chart. Although this may look somewhat daunting, the basic concept is simply that a complex impedance (an impedance comprising both real/resistive and imaginary/reactive components) can be mapped into a circular space in which the horizontal axis represents resistance (the real part) and the outer circumference represents reactance (the imaginary part).

Positive values of reactance (i.e., inductive reactance) appear along the upper semicircumference while negative values of reactance (i.e., capacitive reactance) correspond to the lower semi-circumference. Imaginary (reactive) components are preceded by the letter, j, the sign of which can be either positive or negative according to whether the reactance is inductive or capacitive.

Some fundamental components are shown together with their Smith Chart representation in Figure 3. A pure resistance identical to the system’s characteristic impedance is shown in Figure 3(a) whilst short and open circuit connections are respectively shown in Figures 3(b) and 3(c).  

Pure inductance and pure capacitance are represented by points on the circumference as shown in Figure 3(d) and Figure 3(e). Because their reactance changes with frequency they are shown as lines rather than dots, with the arrow on the line showing the direction of increasing frequency.

Finally, Figure 3(f) shows a series combination of pure inductance and pure capacitance. Note that the impedance of this combination will become zero at the frequency of resonance, f0. This is the resonant frequency at which both the inductive and capacitive reactance will become equal but of opposite direction and cancel each other out. 

If you’re unfamiliar with the term, just remember that it’s used to indicate the reactive part of an impedance (and is a way of expressing the square root of -1). If you’re not too happy with the notion of “imaginary” numbers just remember that, when the sign of the j-term is positive a component will be inductive and, conversely, when the sign of the j-term is negative a component will be capacitive.

All practical RF components and antennas exhibit complex impedances where both resistance and reactance are present and thus can be represented using j-notation. Importantly, complex impedance will vary with frequency due to the changing values of reactance present.

Consider the case of a component that can be represented by a resistance of 50 Ω connected in series with an inductance of 100 nH. At 100 MHz the reactance of the inductor will be approximately 63 Ω and the component will have an impedance that can be expressed as (50 + j63) Ω. At 140 MHz the component’s inductive reactance will increase to 88Ω and so the impedance will then be (50 + j88) Ω. Corresponding impedance values for a resistance of 50 Ω connected in series with a capacitor of 20 pF will be (50 – j80) Ω at 100 
MHz and (50 – j57) Ω at 140 MHz.

To cater for any given value of characteristic impedance the values plotted on a Smith Chart must first be normalized by simply dividing the real/resistive and imaginary/reactive parts by the value of characteristic impedance. So, for example, an impedance of (50 + j25) Ω will be plotted as (1 + j0.5) Ω. Conversely, an impedance of (50 - j25) Ω will be normalised to (1 - j0.5) Ω. These conjugate points are shown plotted in Figure 4. 

Standing Wave Ratio

Standing wave ratio can be easily shown on a Smith Chart by superimposing circles of constant SWR on the chart, as shown in Figure 5. Note that a unity value of SWR corresponds to a circle of zero radius (i.e., a point at the exact centre of the Smith Chart) while infinite SWR corresponds to the outer perimeter of the chart. When used as a tool to investigate matching, the RF designer will invariably strive to ensure that load impedances are as close to the centre of the Smith Chart as possible. Being able to see this all going on in “real time” makes antenna adjustment a real breeze! 

Impedance - Frequency plots

Smith Charts are often used to visualise the behaviour of antennas and RF components over a range of frequencies. Figure 6 shows an example of the analysis of a component in which the normalised impedance varies from (0.23 – j0.65) Ω to (0.75 + j0.41) Ω over a frequency range extending from 110 MHz to 130 MHz. Note how the antenna becomes purely resistive 
at 120 MHz and how the SWR of the antenna has fallen below 2 above 130 MHz. 

Antenna Analysis

A low-cost vector network analyser (see Figure 1) can provide a quick check on the characteristics of an antenna and its feeder. Figure 7 shows some typical results of the analysis of a 130 MHz quarter wave antenna in a 50 Ω system. The analyser’s frequency sweep has been set from 120 MHz to 135 MHz with markers displayed at 120 MHz, 125 MHz and 130 MHz. From Figure 8 we can quickly determine that: 

• The antenna’s SWR is less than 2 over the entire scan range
• The antenna is purely resistive at 123 MHz and 133 MHz 
• The lowest SWR (1.6 approx.) is achieved at 130.5 MHz and the best match to a 50 Ω 
  system is obtained at this frequency. 

In this quick introduction we have only scratched the surface of what can be done with a VNA. If you make use of one of these handy gadgets regularly you will soon wonder how you ever managed without one! 

Credits - Mike G8CKT, HARC

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