# Transient Analysis for Circuits with SPICE Simulations

May 30, 2019

Any engineer that remembers their college days probably remembers spending hours solving circuit analysis problems in the time domain by hand. Extracting and graphing the transient response of complicated circuits can quickly become intractable if worked out by hand. Instead, you can conduct transient analysis for circuits in the time domain using a simulator. You won’t even need coding skills if you use the right software.

Transient analysis is extremely useful for analyzing a circuit’s response due to an AC or DC driving voltage. Although most people will opt to examine the behavior of a circuit driven with an AC source in the frequency domain, it is difficult to examine the transient behavior without further calculations. Instead, you can examine the response in the time domain using transient analysis for circuits with a SPICE simulator.

## What is Transient Analysis?

Transient analysis is all about determining how a circuit responds to changes in the driving voltage/current. Real circuit response to changes in the driving voltage can be hard to predict due to capacitance and inductance within the circuit. In some circuits, the parasitic capacitance and inductance can be large enough that the response of the circuit deviates from the value that was intended based on the design.

Looking at this from the other direction, you can use transient analysis to verify that your circuit responds in the way you intended to a variety of voltage sources. You can examine the following behavior using transient analysis:

• The approach to the steady state over time when driven with a constant (DC) voltage

• How the current and voltage in the circuit change when a DC voltage/current source changes in magnitude

• How the phase and magnitude of the current and voltage differ from those of the driver in an AC circuit

• How the circuit responds to arbitrary driving waveforms in the time-domain

## The Approach to Steady State and Transient Response

Most people are familiar with transient analysis in an RC series circuit driven with a DC source. When the DC source switches on, the charge accumulates on the capacitor and the voltage is dropped entirely across the capacitor. The current in the circuit eventually falls to zero, as does the voltage drop across the resistor. This behavior occurs as the circuit approaches a steady state.

Similarly, in an RL series circuit, the inductor induces back-EMF once the DC source switches on, causing a transient response in the current. The current slowly rises up to its steady state value defined by Ohms law, while the voltage drop across the inductor slowly drops to zero. The voltage is dropped entirely across the resistor. Some people cite this circuit to state that an inductor stores energy, but this is not actually the case as the voltage drop across the inductor is zero, according to Kirchoff’s current law.

Once the DC source in these two types of circuits switches off, the current in the circuit slowly dies out. In the RC series circuit, stored charge leaves the capacitor and slowly falls to zero as the capacitor discharges. In the RL series circuit, the inductor induces a current as the source switches thanks to Faraday’s law. The current also slowly falls off to zero over time.

In these circuits, the current and voltage are exponentially rising or falling functions in time. The amount of time required for the current and voltage to rise/fall to their maximum/minimum values is theoretically infinite. What is really important in transient analysis is determining the time constant for this process. This value tells you how fast the exponential curves describing current and voltage rise or fall over time.

## Transient Response for Circuits with an Arbitrary Source

Circuits driven with an arbitrary source in the time domain also exhibit a transient response in the time domain. In more complicated circuits, including simple RLC circuits where elements are not always resolvable using rules for combining elements in series and parallel, the transient response can be calculated from a second order differential equation with the appropriate initial conditions and source term. The source term in this case can be any waveform you like: an impulse, a constant DC source, a harmonic AC source, a series of digital pulses, a triangle wave, or a non-periodic voltage/current source.

Transient current response in a series RC circuit driven with a series of digital pulses

As an example, the figure above shows how a series RC circuit responds to a series of digital pulses as calculated with a SPICE simulation. This circuit is driven with a 5 V square wave and contains a 100 Ohm resistor in series with a 20 pF capacitor. The current in the circuit (orange curve) shows a transient response with a 2 ns time constant as the driver switches between ON and OFF states, which matches the calculated RC time constant for this circuit.

As transient analysis is essentially a time domain simulation, you can use it to examine the phase and magnitude of the current in any circuit that is driven with a harmonic AC voltage/current source with specific frequency. Working with a SPICE simulator that includes a GUI allows you to place probes at specific places in the circuit, which provides the current at that location. You can also take voltage drop measurements across specific components in the circuit, yielding a graph in the time domain similar to that shown above.

With circuits that have a natural resonance, you can use transient analysis to determine the level of damping in the system as well as the natural resonance frequency. A perfect example is an RLC series circuit that is driven with a DC source. The current in this circuit will exhibit either a overdamped decay, perfectly damped decay, or an underdamped oscillation as it approaches the steady state. Transient analysis allows you to extract the decay constant and the natural resonance frequency from a graph of current or voltage in the time domain.

The same idea applies any linear time invariant circuit driven with an arbitrary waveform. These driving sources do not need to be periodic in time. Rather, they can be arbitrary periodic (sawtooth, quadratic, etc.) or non-periodic sources. A great example from power integrity analysis involves examining the effect of RC filtration and smoothing in a rectifier circuit. Transient analysis with this circuit allows you to extract the ripple voltage. This waveform with ripple can then be used to examine the transient response of a regulator or filter for a power supply.

Transient analysis for circuits can be used to simulate power supply regulation

Transient analysis for circuits does not have to be complex when you use OrCAD PSpice Designer from Cadence. This unique package will take data directly from complex PCB designs, allowing you to easily simulate and analyze the transient behavior of circuits in your schematic and/or PCB.

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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