# Considering a Sinusoidal Source in Circuit Analysis and Design

Let’s go back to the 1880’s, when Nikola Tesla and Thomas Edison were waging the War of Currents. The competition between these two feuding inventors would eventually give way to widespread power distribution systems in urban areas. Tesla would eventually win the day, and AC power systems would become the primary method for distributing power across long distances with minimal losses.

AC sources form the foundation of modern electric power distribution, but plenty of other devices use or are powered by AC signals. Designers and engineers need tools that can consider a circuit’s response to a sinusoidal source in circuit analysis. The right simulation tools can help a designer examine how a circuit responds to an AC voltage or current source and modify their design as necessary.

## Considering a Sinusoidal Source in Circuit Analysis

There are a number of important circuit analysis tasks that involve the response of a circuit to AC signals. There are several analyses you can conduct with circuits that involve an AC source. These analyses include several tasks in the time and frequency domain. Some tasks are much easier to perform in the frequency domain rather than the time domain, meaning you will need to examine how the circuit responds to sources with various frequencies.

In SPICE simulations, you can easily include a sinusoidal source (AC Sources) in your simulation, either as a current source or a voltage source. In addition to a single sinusoidal current source, a powerful circuit simulator allows you to include multiple sinusoidal sources in a single circuit, allowing you to explore how your circuit responds to modulation (i.e., beating or amplitude/frequency modulation). This is useful for designing simple demodulator circuits that do not require a conversion to a digital signal.

Going beyond a single sinusoidal signal allows you to examine how your circuit responds to more specialized inputs, such as signals with frequency modulation, phase modulation, chirp, or dispersion. If you are familiar with Fourier analysis, you’ll know that these waveforms and pulses can be defined in the time domain by calculating the Fourier transform from the frequency domain, and vice versa. A powerful SPICE package will give you considerable latitude to calculate the response in your circuit to arbitrary waveforms.

*Time domain signal produced from a SPICE simulator*

## Understanding and Using Frequency Sweeps

Sweeping through a range of frequencies for your sinusoidal source in circuit analysis allows you to examine how the circuit responds to sources different frequencies. SPICE simulators with a GUI allow you analyze the behavior of your circuit over a range of frequencies. You can specify the minimum and maximum frequency values, as well as the number of steps between these values.

Once you place probes in different locations in your circuit, a frequency sweep will produce graphs showing the voltage and current at these locations as a function of frequency. You’ll receive a graph showing the amplitude and another showing the phase of the voltage and current in the circuit. This then allows you to determine at which frequencies the elements in this portion of the circuit exhibit capacitive or inductive impedance.

Once you conduct a frequency sweep, you can take the response spectrum (both amplitude and phase) and use this to construct a Bode plot. This standardized plot nicely summarizes how your circuit responds to different frequencies and can reveal more information than a linear plot, especially in filter and amplifier design.

## Impedance Spectra for Matching Networks

One important task involved in analyzing circuits driven by AC sources involves determining the impedance spectrum for a circuit. Capacitors and inductors have complex reactance rather than resistance, and the reactance imposed by a circuit element depends on the value of the driving frequency. In high speed design, determining the impedance spectrum for a circuit helps you design an impedance matching network for a certain portion of the circuit or in an interconnect.

This is important for suppressing signal reflections at impedance discontinuity, which can cause signal integrity problems in high speed circuits. The impedance spectrum allows you to determine the exact impedance of the circuit at a specific frequency. This involves calculating the voltage and current across a particular element or set of elements in your circuit, which can then be used to calculate with impedance with Ohm’s law.

*Antenna design is just one area that uses impedance matching for a sinusoidal source in circuit analysis*

Once you’ve determined the impedance at the frequency of interest, you can start to design an impedance matching network for this circuit. There are several types of matching networks. When designing a matching network, you’ll need to calculate the new impedance with the connected matching network at the frequency of interest. You can then tune the resistance values for the circuit to just the right values such that the circuit is matched to a desired impedance.

While some time and frequency domain analyses in simple circuits involving harmonic sources are easy enough to work with on paper, using a SPICE package simplifies time and frequency domain analysis of more complex circuits. The OrCAD PSpice Simulator from Cadence allows you to include a sinusoidal source in circuit analysis and automates many important analyses for a number of applications. This unique package is adapted to complex PCB designs and interfaces directly with your design data.

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