# Using a Varactor Diode In a Tuning Circuit

February 6, 2020

The tuners in these TVs use a varactor diode to select channels

If you’re part of my generation, then you remember the old TV sets with the bunny ear antennas and the knob you had to use to change channels. Nowadays, everything in a TV is digital, but the tuning circuit in an old TV has many applications outside of finding cartoons to watch on Saturday morning. The important circuit element that makes this work is a varactor diode.

A varactor diode has other applications outside of TV tuners, ranging from frequency synthesis to precision RF oscillators. With the right simulation models and tools, you can analyze signal behavior in circuits with a varactor diode in the time domain and determine the best tuning parameters.

## What is a Varactor Diode?

A varactor diode is a simple variable capacitor that allows oscillator circuits and other circuits to be easily tuned by applying a voltage. These diodes have a similar structure as a p-n diode; the structure of a varactor diode is rather simple and illustrates its power as a component with nonlinear reactance. These diodes have a p-n-n+ structure, where the applied voltage modulates the width of the depletion region between the p and n+ sides. When run with a AC small signal that have a high DC offset, it functions very nearly as a linear component with minimal signal distortion.

A varactor diode is run in reverse bias, where an applied voltage changes the width of the depletion region. When the reverse bias voltage is increased, the width of the depletion region also increases, which decreases the capacitance. The image below shows the schematic symbol and capacitance equation for a varactor diode.

Schematic symbol for a varactor diode and capacitance equation.

The exponent in the denominator γ is akin to an ideality factor in a standard diode, ɸ is the diode’s built-in voltage, and C0 is the diode’s capacitance at zero applied voltage. These parameters can be easily determined from measurements of the capacitance versus applied reverse-bias voltage, as long as the built-in voltage is known. This is normally done using a log-log plot, which will be a linear function of log(1 + V/ɸ). An example is shown below for C0 = 1 pF. In this plot, γ will be the negative slope of the resulting line, and log(C0) is the y-intercept. The blue curve is for a varactor diode with γ = 1.25, and the orange curve is for a varactor diode with γ = 1.75.

Capacitance vs. voltage data for two varactor diodes (blue: γ = 1.25, orange: γ = 1.75).

Note that varactor diodes also have some parasitic series resistance R, which will set the maximum useful frequency at which the above equation is applicable. This frequency is just equal to 1/(2πRC0).

## Applications of Varactor Diodes

The applications available for use with a varactor diode depends on the range of DC and AC voltages used in a circuit. In a simple DC circuit, you only need to worry about the capacitance as a function of input voltage. Varactor diodes are rated to run up for dozens of V in reverse bias; exceeding this value can cause the varactor diode to run highly nonlinearly, breakdown, or both.

For applications requiring tuning of RF circuits, circuits with varactor diodes will use an input AC signal that has some DC offset (Vdc). Let’s look at three different ranges for applications of varactor diodes in terms of the peak-to-peak voltage of the AC input (Vp-p) and the DC offset.

### Vp-p << Vdc, Large Vdc

The tunable nature of a varactor diode makes it ideal for use in tunable RF oscillators, filters, and impedance matching networks (e.g., LC tank circuit) when Vp-p << Vdc. In this application, the peak-to-peak voltage should be less than the DC offset to avoid changing the capacitance of the varactor by too much during an oscillation. In other words, the capacitance of the varactor can be regarded as constant in these applications. The capacitance of the varactor is changed by adjusting the DC offset. Many commercially available varactor diodes are rated to run at hundreds of MHz, allowing them to be used in the three application areas mentioned above.

If you look at the capacitance vs. voltage on a linear scale, you can determine the appropriate range for a linear operating region. The graph below shows capacitance vs. voltage data for the two example varactor diodes shown in the graph above.

Capacitance vs. voltage data for two varactor diodes on a linear scale (blue: γ = 1.25, orange: γ = 1.75).

From this graph, we can see that a higher DC offset should be used as this will keep the capacitance nearly constant as the AC component oscillates. This allows a circuit to be tuned with quite stable capacitance. The output can then be passed to a filter or amplifier to extract the desired signal.

### Vp-p ~ Vdc, Small to Large Vdc

In this range, the capacitance is highly nonlinear as a function of Vdc. This range is normally used for parametric amplification and frequency synthesis with analog PLLs. Specifically, the nonlinear impedance of the varactor diode will generate higher order harmonics, which are then passed to the output port of the circuit. The desired harmonics can then be retrieved with a high-Q bandpass filter.

## Modeling Tuning Circuits with Varactor Diodes

Because varactor diodes are nonlinear components (i.e., they have nonlinear impedance), the easiest simulation methods you can use to examine the behavior of these components is transient analysis in the time domain. Note that pole-zero analysis is useless in these circuits as transfer functions and Bode plots are only defined for linear circuits. Therefore, you would have to look at the behavior of a circuit in the time domain using transient analysis. This will allow you to identify stability, which is a critical aspect of parametric amplification in RF systems. Once you have some time-domain data, you can use a Fourier transform of the data to examine any higher order harmonic content generated in the circuit.

Another option is to use small signal analysis to convert the nonlinear circuit to a linear circuit, where the DC offset is the operating point. This allows you to explore the Vp-p << Vdc, small Vdc regime and obtain reasonably accurate results. You can then examine the behavior around different operating points using AC and DC sweeps.

When you need to build highly precise tuning circuits, you need to work with the best PCB design and analysis software. The simulation tools in PSpice Simulator for OrCAD and the full suite of analysis tools from Cadence are ideal for analyzing the behavior of any circuit with a varactor diode. You’ll also have access to manufacturer part search tools as you prepare to source components for your system.

If you’re looking to learn more about how Cadence has the solution for you, talk to us and our team of experts.

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