PCB Blog - Transient Signal Analysis in PCB Board Design

Transient responses in interconnects and on power lines in PCB board are the cause of bit errors, timing jitter, and other signal integrity issues. You can determine the design steps to take in designing the perfect circuit using transient signal analysis. Transient signal analysis in simple circuits can be manually checked and calculated, allowing the transient response to be plotted over time. More complex circuits can be difficult to analyze manually. Instead, you can use the simulator for time-domain transient signal analysis during simulator design. You don't even need coding skills if you use the right design software. Formally, transients may occur in circuits that can be written as a set of coupled first-order linear or nonlinear differential equations (autonomous or non-autonomous). The transient response can be determined in several ways.

A transient response without feedback in a time-invariant circuit falls into one of three situations:

1) Overdamped: Slowly decaying response, no oscillations

2) Critical damping: fast decay response, no oscillation

3) Insufficient damping: damped oscillatory response

For circuit simulation, you can run transient signal analysis simulations directly from the schematic. This requires consideration of two aspects of circuit behavior:

1) Drive signal. This defines the change in input voltage/current level that causes the transient response. This could involve a change between two signal levels (i.e. switching digital signals), a dip or spike in the current input signal level, or any other arbitrary change in the drive signal. You might consider driving with a sinusoidal signal or an arbitrary periodic waveform. You can also consider the finite rise time of the signal as it switches between the two levels.

2) Initial conditions. This defines the state of the circuit when the drive signal fluctuates or the drive waveform is turned on. Assume that at time t=0, the circuit is initially in a steady state (ie, there is no previous transient response in the circuit). If no initial conditions are specified, the voltage and current are assumed to be zero at t=0. After running the simulation, you will be given an output that overlays the input signal and output, allowing you to see exactly how different changes in signal level produce transient responses. An example of switching digital signals is shown below. In this circuit, we assume that the initial conditions are not specified. The transient response of the current exhibits severe overshoot and undershoot due to insufficient damping. One solution here is to add some series resistance at the source to increase damping. A better solution is to reduce the inductance or increase the capacitance in the circuit to bring the response into a damped state.

Transient signal analysis after schematic and layout

The output is similar to that seen in the reflected waveform simulation, where the incident and reflected waves are compared in a post-layout simulation. The difference, in this case, is that we are working on a schematic that does not take into account parasitics in the PCB board. In a post-layout simulation, parasitics are considered and your transient signal analysis results may inform you to make some changes to the layout or stack up to reduce the ringing described above. If the above results are seen in the post-layout signal integrity simulation of the transmission line, one solution is to reduce the loop inductance in the interconnect and scale down the capacitance. This will increase the damping of the circuit without changing the characteristic impedance. This also moves the resonant frequency in the circuit to a higher value, reducing the ringing amplitude. Another option is series termination at the driver.

Pole Zero Analysis

An alternative to time domain simulation is to use pole-zero analysis. This technique brings the circuit into the Laplace domain and computes the poles and zeros in the circuit. This allows you to immediately see how the transient signal response behaves in the circuit. Note that this type of simulation can still take into account the initial conditions in the transient signal analysis, so the results are more general. However, you cannot directly see the magnitude of the transient signal because you are not explicitly considering the behavior of the input waveform.

Stability and Instability in Transient Signal Analysis

One thing to be aware of here is the possibility of instability in circuits containing feedback. In a typical circuit, you will check the PCB schematic and layout, you will almost always encounter stable transients. The example above shows a stable response. Despite transient oscillations, the signal eventually decays to a steady state. In circuits with strong feedback, transient oscillations can become unstable and grow over time. Amplifiers are a well-known situation where thermal fluctuations or a strongly underdamped response in the presence of strong feedback can drive the amplifier's response to becoming unstable and saturated. A saturated nonlinear time-invariant circuit will eventually force this unstable amplitude to settle to a constant level. In transient signal analysis, you can easily spot instabilities in the time domain; this will appear with an exponential increase in the output in an underdamped state. In pole-zero analysis, the real part is positive on the PCB board.