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# What You Can Learn From a Frequency Sweep Test

### Key Takeaways

• Frequency sweeps are only defined for linear time-invariant circuits.

• With a frequency sweep, you can extract the bandwidth of a circuit or system, and you can generate a transfer function.

• Nonlinear circuits require more sophisticated simulations, or they require complex iteration in the time-domain. Poles and zeros for a circuit can be determined from a frequency sweep test.

Time-domain and frequency-domain simulations are the two fundamental tools for examining the behavior of your electronics. As their names suggest, time-domain analysis is all about examining what happens to a specific signal over time, regardless of its bandwidth. This gives you a comprehensive view of circuit behavior in the time domain, and you’ll have an opportunity to quantify things like signal distortion and attenuation, simply by comparing input and output signals.

Analog engineers generally work in the frequency domain. The goal in designing analog electronics is to manipulate different frequencies with your circuits, and the fundamental tool used in these simulations is a frequency sweep test. When you have access to a powerful electronics simulator with verified component models, you can examine how your system responds to different frequencies.

## When to Use a Frequency Sweep Test

Frequency sweep tests are decidedly in the realm of analog electronics. The goal is to analyze how an input monochromatic signal is affected by different components in a circuit. The frequency of the input signal is then swept throughout some desired range, and the output voltage or current at each input frequency value is recorded. Circuits with reactive components will also apply a phase shift to the signal, and the phase shift is recorded alongside the magnitude of the output voltage/current.

A frequency sweep test can normally be performed with linear time-invariant circuits without invoking any approximations in circuit behavior; nonlinear circuits can be examined with some other advanced analyses (see below). Passive components are already defined in SPICE simulators, but you can also evaluate circuits with integrated circuits using verified component models in your simulator. The results from a frequency sweep test can be used in the following ways:

• Construct a transfer function. This is the most common use of a frequency sweep. The transfer function is equal to the output voltage divided by the input voltage at each frequency. The magnitude and phase of the transfer function are plotted in their own graphs.

• Extract the input impedance of the circuit. Simply divide the input voltage spectrum by the current entering the equivalent circuit to get the input impedance spectrum.

• Identify the bandwidth of the circuit. When the magnitude of the input admittance is plotted on a logarithmic scale, you can extract the bandwidth of the circuit. The bandwidth is normally defined as the frequencies where the admittance drops by 3 dB below the peak admittance. Gain provided by an example amplifier circuit. The bandwidth can be easily extracted from the 3 dB point in frequency sweep test results.

Compared to time-domain analysis, a frequency sweep test provides some important advantages. Examining a signal in the time-domain requires manually extracting the impedance and phase difference at specific input frequencies, which is time-consuming.

However, a time-domain analysis is advantageous for examining how a broadband signal is affected by a linear circuit; you can overlay and directly compare the two signals in the time-domain. For nonlinear circuits with arbitrary signals, you need to use more advanced techniques to understand the frequency behavior-dependent behavior of your circuits.

## Nonlinear Circuits: Where Frequency Sweeps Fail

A frequency sweep test is only defined for a linear time-invariant circuit, or for a non-linear circuit that runs in the linear regime, thus nonlinear circuits need more sophisticated techniques to understand circuit behavior. When we say a circuit is “nonlinear,” we mean the output voltage/current is a nonlinear function of the input voltage/current. The output frequency is generally a linear function of the input frequency, even in nonlinear circuits.

Nonlinear circuits have complicated frequency-domain behavior due to the generation of additional harmonics in the input signal. In order to examine the frequency-dependent behavior of a nonlinear circuit, you need to use one of the following analyses:

• Small-signal analysis. This involves approximating the behavior of each component in the circuit as a linear function of the input. These approximations are only defined around some operating points and are only valid for “small” input amplitudes. When you conduct a frequency sweep test at each input level, you can acquire a transfer function and you can construct a graph that shows how the transfer function changes as the input voltage level changes.

• Harmonic balance. This is a more complex simulation that divides a nonlinear time-invariant circuit into its linear and nonlinear portions. An arbitrary time-dependent signal is decomposed into its dominant frequency components, and this input spectrum is passed into the nonlinear circuit. The nonlinear portion will generate additional harmonics at the output. This is not quite the same as frequency sweep, but you can iterate through different frequencies and recreate some results for a typical frequency sweep test. This technique is much more powerful than small-signal analysis, but it requires manual iteration.

For continuous time-variant circuits, i.e., where the behavior of the circuit varies smoothly in time, you’re stuck working in the time domain while considering initial conditions in the system. Simulation results may be very sensitive to the initial conditions in the system, and stability of the system needs to be analyzed carefully. When coupling is present in the system, you’ll need to carefully analyze how the coupled quantities converge or diverge to/from an equilibrium solution, or if they produce a limit cycle in phase space. These topics remain an active area of mathematics and engineering research.

When you need to examine how your circuits respond to different frequencies, the best PCB design and analysis tools and front-end design features from Cadence integrate with the powerful PSpice Simulator. You can easily perform frequency sweep tests and simulate circuit behavior. Once you’ve created your layout, a set of SI/PI Analysis Point Tools can be used to generate post-layout simulation results for comparison with your pre-layout simulations.