 # Measuring Slew Rate or Rise Time

From time-to-time questions arise—mostly related to power amplifiers—about slew rate and how to measure it. In this post, we discuss the mechanism of slew, and the basic measurement.

Slew rate is the maximum rate at which an amplifier output can change, with an input signal applied that very quickly steps from a minimum output level to a maximum output level. For very dynamic content, the amp output is required to faithfully reproduce all frequencies and amplitudes. Ideally, the amplifier output would change levels instantaneously, but capacitance in the amplifier output stage generally limits how fast that transition can occur. Slew rate is specified as a change in amplitude with respect to time (dV/dt), typically shown as V/µs. Slew rate is considered a large-signal performance measurement, as opposed to rise time which is a small-signal performance measurement.

In both analog and digital amplifiers, the slew rate limit is generally set by the current available to charge or discharge capacitance in the amp or the connected output load. Normally, the transition time measurement is made from the 10% to 90% output range. For example, if you had an amplifier with a maximum output amplitude of 10 Vpk-pk centered around 0 V, you would measure the transition time from -4 V to +4 V.

There is a relationship between rise time and bandwidth. One approximation for this is:

-3 dB BW = .35/Tr

As an example, the power amp DUT (Device Under Test) I use in this discussion is shown later in this article to have a rise time of about 5.84 μs. Using the above formula indicates we should see a bandwidth of about 60 kHz. Here is a swept sine measurement of bandwidth for this unit, showing the actual bandwidth at 53.2 kHz: ## Making the measurement

A square wave signal generator or a step generator, which is much faster than the DUT, is required to make a slew measurement. The generator should also be able to apply an amplitude that will drive the DUT near its limits. Fortunately, most power amps have some amount of gain, so a generator output amplitude in the range of a few volts is generally suitable. The measurement device must also have enough dynamic range, bandwidth, and timing resolution to make the measurement.

Options AG52 and BW52 are required for making slew tests using APx500 series analyzers (specifically the APx525, 526, or 555). AG52 is a high-performance analog generator that provides a very pure square wave signal generator which can be used for testing rise time and/or slew rate, and BW52 extends the bandwidth of the analyzer to 1 MHz. Both are options available for APx525 and APx526 analyzers, while both the AG52 and BW52 come standard on APx555 analyzers. The rise time from the AG52 square wave generator is consistent for all output levels. Here is a graph that shows the source rise time performance for the full range of the output: Just to confirm that what I measured on the analyzer was the source performance (not degraded by the analyzer measurement side), I connected the APx generator’s square wave output directly to a 200 MHz bandwidth scope and measured the same 1.6 μs risetime.

The intrinsic slew rate of the APx555 is dependent on the amplitude of the signal from the APx555 Generator. Here is a graph showing this perspective: In essence, this chart shows that the analyzer itself is still showing small-signal rise time even at maximum output on the generator.

To make slew rate measurements, it is important to set the analyzer to 1 MHz bandwidth, and remove all filters from the signal path setup. The following image shows the key areas to set in the “Signal Path Setup” on the APx analyzer. The dV/dt can be measured by placing cursors on the scope monitor of the analyzer and setting the cursors at the 10% and 90% of pk-pk points. Here is the typical rise time from the AG52 generator with the square wave selected, 1 MHz bandwidth, and all filters removed: As indicated in the Cursors legend in the lower right portion of the plot (ΔDelta), the plot shows a dt of 1.602 µs, and a dV of 9.046 V.

Note the very clean transition, with no overshoot or ringing. This measurement demonstrates a generator slew of 9.046 V/1.602 µs, which is approximately 5.65 V/µs.

Next, we move to testing a Class D switch-mode power amp. Here is an example of a slew rate measurement from class D switch-mode power amp: In this case, the DUT contains output filters that are used to remove most of the high frequency switching content from the output signal. The ripple that can be seen is the residual switching signal coming through the DUT’s low pass output filter. For other DUTs, it may be necessary to add a switching amplifier measurement filter to remove this high frequency content from the measurements. These filters might have some impact on the maximum slew rate.

Here you see that the DUT exhibits some overshoot and has a transition time of 5.84 µs. The cursors show the delta volts at 10% and 90% of 10.05 Vpk-pk. The slew rate can then be calculated as 10.05/5.84 with units in V/µs, or approximately 1.72 V/µs. Using the APx555 may not be adequate for the very highest bandwidth power amps but should be adequate for most other devices.

There is a linkage between slew rate and bandwidth, which is stated with this equation:

Frequency (max) = SR/(2*π*Vpk)

For this DUT, we measured the slew rate at 1.72 V/µs, and the output was 10 Vpk-pk, or 5 Vpk. Plugging these values into our formula above produces a result of 54.8 kHz, which correlates reasonably well with the measured bandwidth from earlier in this discussion.

In the following plot, I have shown the slew response curve of the DUT amp relative to the input amplitude. We see that the slew rate is linear out to about 1.7 Vpk-pk input level. Beyond that, the amp output becomes clipped. So, for this DUT, evaluating the slew rate at 1.7 Vpk-pk is the best point to get large signal swing performance, while keeping the DUT in a linear operating mode. The slew rate measured 1.675 V/µs.

Alternatively, it is also reasonable to use a digitizing oscilloscope and a high-performance signal generator to make the measurement. Oscilloscopes with very high bandwidth are readily available and many offer a dV/dt measurement. Signal generators are available with fast edges, including conventional step or square wave generators and arbitrary waveform generators. If the DUT is a power amplifier, it is likely that you would need a generator that can output an amplitude of 2-5 volts while maintaining the fast edge. Power amps often have a gain in the 10x to 30x range, so you would need an oscilloscope with attenuation adequate to acquire a 40 V to 60 V (or perhaps higher) signal, and bandwidth to support the fast edges.

## The relationship between gain, rise time, and slew rate in an amplifier

It is fairly common in conversations about slew rate for a question to be posed about how the gain affects the rise time. Though the gain multiplies the signal amplitude, it does not multiply or divide the rise time. The amplifier is expected to produce a faithful reproduction of the exact spectral content of the source signal. In the case of the square wave source, the min and max level values are DC for the duration at that level. All of the AC (spectral content) is in the transition edge. In the case of a very pure square wave, this is the odd harmonics of the fundamental tone that extend out to the bandwidth limit of the system.

Having said that, gain does have a multiplying effect on slew rate, because it increases the total voltage swing, thereby increasing the numerator of the slew rate equation (V/µs) and therefor increasing the slew rate. This can be seen in the “Slew Rate vs Output Amplitude” chart previously discussed.

## Dynamic Intermodulation Distortion (DIM) and Transient Intermodulation Distortion (TIM)

DIM and TIM are used interchangeably to identify a test technique that combines a square wave source and a sine wave source as a combined, highly-dynamic stimulus to an amplifier, enabling a test for intermodulation distortion between the two source signals through the DUT. While this is not directly related to slew rate testing, it can be done using a similar set of equipment. For example, the same APx555 that I used in the above slew rate examples has all the needed equipment to make these measurements. The basic concept behind this test is that a very high transient source (square wave) and a sine source can combine to produce a signal that better represents the highly dynamic spectral content in some audio content. The DIM measurement is defined in the standard IEC 60268-3, sec. 14.12.9. The DIM measurement can be selected from the APx500 software via the “add measurement” button in the sequence setup in Sequence Mode, or by selecting “IMD Type: DIM” in Bench Mode.