# Gain-Phase Plots in Active Circuit Analysis

Active components and circuits do more than just modulate an output based on two or more input signals. Active components can also have gain, which is sometimes implemented via a feedback loop. Feedback in electronic systems goes along with phase, referring to the fact that a feedback loop can create different phase shifts and amplitude changes at different frequencies.

If you're selecting components for use in a circuit with feedback, you will need to evaluate the component and completed circuit based on a gain-phase plot. Here's how to use this information from a data sheet to evaluate a component, as well as gain-phase data to evaluate a circuit in simulation or measurements.

## How to Read a Gain-Phase Plot

Gain-phase plots show two important quantities in systems with feedback, or in active systems with voltage/current gain. These plots are essentially the two components in a Bode plot, and they show the following information:

• Gain through the circuit or in a feedback loop, defined in terms of voltage or current

• The phase of the signal measured at the output node with respect to the input node

When using amplifiers or active filters that use feedback loops, the gain refers to the loop gain, which could further refer to the open-loop gain or closed-loop gain. Typically, when selecting a component for use in a circuit, we look at the gain-bandwidth product and the open-loop gain to determine if the amplifier will be appropriate for a particular circuit. When evaluating a circuit design, we typically refer to the closed-loop gain, or the gain with components and parasitics included in the feedback loop.

The various components in a feedback loop create a transfer function once the loop is closed. This then gives a feedback loop's gain-phase curve its particular shape as a function of frequency. These curves are actually complex functions, so there will be a magnitude and phase associated with a transfer function. This gives us the gain-phase plot when the two curves are overlaid on top of each other as a function of frequency.

## How to Simulate Gain-Phase Plots

Gain-phase plots can be simulated very easily using SPICE simulations. This can be done in the time domain with a transient analysis simulation, or in the frequency domain using a frequency sweep simulation.

Transfer functions that make up a feedback loop can have poles and zeros, just like any other transfer function. If the entire closed feedback loop was perfectly resistive, then the gain portion of the gain-phase plot would be linear. It is the reactance, resistance, and parasitics built into the amplifier model and feedback loop that create the particular gain-phase plot.

## Measuring a Gain-Phase Plot

The easiest way to measure a gain-phase plot is with an oscilloscope. Measurements of a gain-phase plot using an oscilloscope can be performed with following process:

1. Hook scope probes onto the input node and feedback closure points on the circuit

2. Configure your oscilloscope to measure both probes simultaneously

3. Input a sine wave into your amplifier-based circuit

4. Measure the time difference between the input and output signals

The time difference and frequency together give a phase difference as follows:

φ (degrees) = fΔt

The gain can be calculated by comparing the input and output amplitudes. When this is performed at multiple frequencies, the data can be overlaid at each frequency point, giving a gain-phase plot. Most digital oscilloscopes will perform the phase, frequency, and amplitude measurements automatically.

## Important Points in Gain-Phase Plot

There are three types of points that are important in gain-phase plots. These are poles, zeros, and critical points.

Poles and zeros have their usual context in terms of transfer functions, and it is very easy to see where a pole or zero arises in a gain-phase plot. In contrast, critical points are specific pairings of gain and phase that lead to stable or unstable behavior. For example, one might observe sustained oscillations at a specific frequency when the circuit is excited by a broadband signal. This can be examined with stability criteria, such as Barkenhaus stability.

A gain-phase plot example from a transimpedance amplifier with specific capacitance values of an input photodiode and feedback loop capacitance is shown below. This is a plot from the OPA818 datasheet, which is a high-frequency transimpedance amplifier with a large gain bandwidth product.

If you are experimenting with an amplifier circuit and you observe a strange oscillation that you did not expect, consider looking at the game phase plot. You just might have excited an instability and created a sustained oscillation that you did not intend.

Whenever you want to build and analyze your amplifier circuits using gain-phase plots, make sure you simulate your designs with the complete set of tools in PSpice from Cadence. PSpice users can access a powerful SPICE simulator as well as specialty design capabilities like model creation, graphing and analysis tools, and much more.

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