# What is Frequency Response Analysis

Application Notes

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Introduction

With many of today’s electronic designs, performing frequency response analysis is often necessary to ensure they meet performance requirements. This domain of signal characterization allows you to observe how the outputs of your circuit designs respond across a broad spectrum of different frequency inputs. Failure to perform such analysis may result in faulty designs and products. Frequency response analysis (FRA) is critical in devices such as passive and active filters, amplifiers, and negative feedback networks of switch-mode power supplies (closed-loop response).

In this application note, you will learn about what FRA is and see three different measurement examples illustrating how to use the application.

What is Frequency Response Analysis?

If you are not familiar with frequency response measurements, remember back to your electrical engineering college days when you were required to create Bode plots. Bode plots are theoretical straight-line approximations of gain and phase versus frequency of a system’s output relative to the input (i.e. frequency response). The plot is based on poles and zeros of the circuit’s transfer function. For example, the transfer function, T(jω), of a series R-L-C passive circuit (Figure 1) will have 2 poles and 1 zero (at 0 Hz). This results in a bandpass filter based on the following formula:

Assuming R = 50 Ω, L = 10 µH, and C = 1 µF, fPole1 theoretically occurs at 3.2 kHz and fPole2 theoretically occurs at 800 kHz. These are the frequencies where the ± 20 dB/decade straight-line approximations intersect 0 dB as shown in Figure 2. But if you tested this passive circuit, you would discover that the actual gain and phase traces would not be perfectly straight lines, especially near these pole frequencies.

You would find that the gain would be down approximately 3 dB and the phase would be approximately ± 45°at each of the two-pole frequencies.

So how do you test a design to verify actual performance versus the theoretical?

Automatic Frequency Response Analysis

Unless you are fortunate enough to have access to a dedicated Frequency Response Analyzer (FRA) or Vector Network Analyzer (VNA), this analysis has historically been a very tedious measurement exercise using an oscilloscope along with a function generator as the sinewave input source. It involved lots of manually-performed amplitude and timing measurements to determine gain (A = 20LogVOUT/VIN) and phase at multiple frequency settings. This is the method that most EE students use today. However, the introduction of Keysight’s frequency response analysis (FRA) application has completely changed this. For the first time, you can perform automatic frequency response measurements using the scope’s built-in waveform generator as a sinewave input source, along with automated in-scope FRA software.

Before you perform a frequency response test to produce a gain and phase Bode plot, you should have a basic understanding of the test parameters in the InfiniiVision scope’s FRA “Settings” menu shown in Figure 3.

Frequency Mode:

o Sweep – The scope performs multiple gains and phase measurements at frequencies ranging from the specified Start frequency to the specified Stop frequency. This produces an overlaid logarithmic gain plot and linear phase plot versus frequency. Measurement results can also be viewed in a table.

o Single – The scope performs a gain and phase measurement at just one specified frequency producing numerical gain and phase test results only (no plot).

Frequency (Start, Stop): The specified Start frequency is the initial test point and can be set as low as 10 Hz. The specified Stop frequency is the final test point and can be set as high as 20 MHz.

Points: The specified number of frequencies to test (1 to 1000) across the Start/Stop sweep range. A higher number of test points provides more resolution; however, it will take longer to plot all the data.

Source (Input, Output): The specified oscilloscope input source (channel-1, channel-2, channel-3, or channel-4) and the specified output source (channel-1, channel-2, channel-3, or channel-4).

WaveGen (Amp, Imp): The specified test amplitude and load impedance. For linear systems, a higher test amplitude will typically provide measurements with a higher dynamic range. But when testing systems that can become saturated and then exhibit non-linearities, such as feedback amplifier circuits, a test amplitude that is set too high can cause waveform distortions and inaccurate test results.

Amplitude Profile: If turned ON the test amplitude can be specified to increase or decrease linearly from decade-to-decade frequencies, as opposed to using a fixed test amplitude across the entire Start/Stop sweep range. This test mode can be useful for optimizing dynamic range when testing systems that can sometimes exhibit non-linearities. Note that amplitude profiling is not available in the 1000 X-Series scopes.