# Slew Rate

#### DonH56

##### Master Contributor
Technical Expert
Forum Donor
<Another old thread reposted, hope it is useful.>

I have seen a few discussions about slew rate and thought it might be a worthwhile thread. Slew rate is defined as the amount a signal (voltage, current, power, whatever) changes in a given time period. For the math types, it is the first derivative with respect to time. For a single-frequency sinusoid, e.g. a single tone, the slew rate (SR) is given by

SR = 2*pi*f*A where
pi = 3.14159…​
f = frequency​
A = amplitude​

The amplitude is the peak (pk) value of the signal. For example, a 1 Vrms signal is 2.828 Vpp or 1.414 Vpk. At 1 kHz, the slew rate is 8,886 V/s, or 0.0089 V/us (Volts per microsecond, a typical unit). This is the maximum slew rate, which occurs at the sinusoidal signal’s center crossing. It decreases away from the center, though stays fairly close to the maximum value for most of the amplitude range (it does decrease to zero at the very top and bottom).

Since slew rate seems to be more a concern for power amplifiers, I calculated the slew rate for various power levels (rms) into an 8-ohm load and plotted it versus frequency below. The log-log plot presents the slew rate as a straight line at each power level (1, 10, 100, and 1k W).

The slew rate may be lower than some expected given the 50 to 100 V/us rates specified by some manufacturers. At 20 kHz, a 100 W signal only requires 5.03 V/us slew rate. There are pros and cons with higher slew rates:

A few pros about high slew rate:
1. Greater design margin for high-frequency signals.
2. A higher slew rate allows the amplifier to better control high-frequency ringing in the load (speaker).
3. Higher slew requires higher bandwidth, which can make it easier to close the feedback loop without instability.
4. Higher bandwidth is usually required both for signal flatness (no roll-off in the audio band) and for low distortion (you need wide bandwidth for low distortion, especially with feedback -- see point 3).
The cons tend to mirror the pros:
1. High slew rates can push design margin to the edge, decreasing amplifier stability.
2. High slew rate can cause excessive high-frequency content, potentially damaging drivers. If the speakers cannot respond quickly enough, power turns to heat that can damage or destroy the drivers.
3. The greater bandwidth required for high slew rates can cause high-frequency peaking and ringing, or even oscillation, with certain loads. Higher bandwidth also means more noise, and more (higher-frequency) distortion components.

HTH - Don

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Hey Don , nice write up.
But i have to ask , why some manufacturers during the 80's and 90's war of amps , were stating some numbers like 350v/us .
Sure they wanted to advertise their super fast amps. Ok that is understood. But since the math type for slew rate exists from some decades back , i wonder what they are doing.

Hey Don , nice write up.
But i have to ask , why some manufacturers during the 80's and 90's war of amps , were stating some numbers like 350v/us .
Sure they wanted to advertise their super fast amps. Ok that is understood. But since the math type for slew rate exists from some decades back , i wonder what they are doing.
My view is that very high Slew Rate figures, like very low THD figures are quoted because they can, and although they may be indicative of a well designed amplifier, such an amplifier won't necessarily sound any better than one with lower/higher but still perfectly adequate numbers.
Pure marketing.

S.

While an amplifier is busy slewing, it is basically running open loop and can't do anything else. That is obviously not desirable, so you do want some headroom. How much is needed is up for debate, but common safety factors include between a factor of 3 and 10 more. For our 100 wpc amplifier, that would be between 15 and 50 V/µs.

Slew rate was also the driving factor behind amplifier frontends moving towards JFET inputs in the early '80s. As those pretty much had to be cascoded as well, this was accompanied by a general increase in performance, which was not unwelcome I imagine. Input pairs were generally undegenerated at the time, so BJTs had a bit of a hard time hitting the slew rates required. And even with input degeneration in place, certain disadvantages remain (e.g. input current noise).

Low slew rate also tends to be associated with a propensity towards unwanted RF demodulation. Traditional undegenerated BJT inputs running at very low current tend to be particularly prone to it, and I'm sure many of us have cursed 1980s power amp ICs when they would reproduce the activity of our phones all too clearly.

Hey Don , nice write up.
But i have to ask , why some manufacturers during the 80's and 90's war of amps , were stating some numbers like 350v/us .
Sure they wanted to advertise their super fast amps. Ok that is understood. But since the math type for slew rate exists from some decades back , i wonder what they are doing.

Ask somebody in Marketing, not me. I tend to agree with the posters above. High slew rate and ultrawide bandwidth were popular marketing differentiators back then, since "bigger is better", but they created as many or more problems than they solved. You need bandwidth well beyond 20 kHz for flat response at 20 kHz to less than a dB, and for low distortion that high, but too much bandwidth leads to greater noise, higher susceptibility to EMI/RFI, and stability issues. It also costs more in power, and higher-frequency transistors usually cost more, but those are minor issues IMO. Noise problems and stability issues would be my concerns, then and now.

In my world of design, you usually want just right of everything for the application. Greatly exceeding the requirements is usually costly, in other specs like noise and stability, if not in dollars and cents. Not everyone needs to use their audio amplifier for AM radio transmission.

IME/IMO/FWIWFM/my 0.000001 cent (microcent)/YMMV/blah, blah, blah - Don

Ok guys point taken.

In layman's terms, does Class D have (dis)advantages with respect to slew rate?

In layman's terms, does Class D have (dis)advantages with respect to slew rate?

Simple answer: no. Since it is a pulse-width modulated output, sort of, very high slew rates are needed to avoid dead time/hysteresis in the output switching devices, but the signal bandwidth is set by the output filter network along with whatever you decide the input bandwidth to be. The output devices do indeed switch very fast, but it is essentially the "envelope" of the pulses that creates the sound, and that is heavily filtered (we hope). Look at the class D 101 thread for more about class D operation. They usually need high feedback, which means greater gain-bandwidth, which may require higher slew rate, but in the end it is usually a wash IMO. You have to filter out the switching noise so early class D designs might actually have worse slew rate due to the output filter; modern design switch fast enough that it's a wash. Again, my opinion, not my day job.

FWIWFM - Don

In layman's terms, does Class D have (dis)advantages with respect to slew rate?
The simplest explanation and details that I could find regarding slew rate for class D and linear amps is from Bruno Putzeys.

The simplest explanation and details that I could find regarding slew rate for class D and linear amps is from Bruno Putzeys.
View attachment 153918

With all respect to Bruno, this is an oversimplification. Output filter is a linear LC(R) circuit and as such has no slew rate limitation. It has corner frequency and corresponding rise time, not slew rate limitation. Switching times of the power stage say nothing about analog signal slew rate of the complete amplifier. This is determined by the input stage SR and control loops responses in the class D modulator. I wonder why Bruno has released such marketing-like info.

Keep in mind that the formula shows slew rate based on a sine wave shaped signal.

With all respect to Bruno, this is an oversimplification. Output filter is a linear LC(R) circuit and as such has no slew rate limitation. It has corner frequency and corresponding rise time, not slew rate limitation. Switching times of the power stage say nothing about analog signal slew rate of the complete amplifier. This is determined by the input stage SR and control loops responses in the class D modulator. I wonder why Bruno has released such marketing-like info.
The slew rate of a passive RC LPF would be the first time derivative of:
E = V × e^(-t/RC ), where E is the instantaneous output voltage at time t.

With all respect to Bruno, this is an oversimplification. Output filter is a linear LC(R) circuit and as such has no slew rate limitation. It has corner frequency and corresponding rise time, not slew rate limitation. Switching times of the power stage say nothing about analog signal slew rate of the complete amplifier. This is determined by the input stage SR and control loops responses in the class D modulator. I wonder why Bruno has released such marketing-like info.
Missed this first time around. In this case (class D amplifiers), the output devices slew very quickly, but generally the output bandwidth is determined by the filter and that determines the effective slew rate of the final (filtered) PWM output. Slew rate of the output devices is irrelevant unless the switching rate is very low. I agree it is not usual to mix slew rate and bandwidth that way but it makes sense to me in this context.

The slew rate of a passive RC LPF would be the first time derivative of:
E = V × e^(-t/RC ), where E is the instantaneous output voltage at time t.
It makes no sense to define slew rate of the passive circuit, as it is amplitude dependent and in fact unlimited (infinite step amplitude will make infinite "slew rate"). That's a big difference compared to active circuits where slewing is limited by stage maximum current that is charging parasitic or real capacitances.
For an RC element please talk about maximum dv/dt, which for the step response occurs at t=0, for a 1st order RC low pass.
[1/RC x e^(-t/RC ) is your expression for V=1 amplitude]

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For class D amplifiers, what matter is TURN-ON and TURN-OFF time, since power dissipations are located there, and hence maximum switching frequency (and thus output filter size) and heatsink requirements.
If power-supply is not built in the amplifier, and you have to provide it externally, actually what you should check is current slew rate (dA/dt). For the 100W amplifier on 8 ohm load, this is about 0,63 A/us @20kHz (but usually you don't need such power at this frequency).
This should not be a problem and can be improved adding large value capacitors at power supply output (if it has not problem with such load).
Take note that if reducing the load value (from 8 to 4 ohm), the voltage slew rate requirement decreases of factor of 4, on the contrary the current slew rate requirement increases of 1,41 factor.

Turn-on and turn-off times for switching devices are usually called rise times and fall times, respectively, and units of time are used in the measurements. The measurement shows the time it takes for a switching voltage to traverse its full range of amplitude, from full on to full off or vice versa. Often, a 10% to 90% portion of the swing is used. Slew rate is the rate, in volts or amps per second at which a signal changes amplitude. Units are voltage or current and time. Slew rate can be measured of the full swing of the signal, or just a portion of that.

The audio signal slew rate of a class D amplifier is (essentially) decoupled from the switching speed of the output stage as discussed in the previous posts. The effective signal slew rate is determined by the bandwidth of the output filter, not the switching speed of the output devices, in a class D amplifier.

Turn-on and turn-off times for switching devices are usually called rise times and fall times, respectively, and units of time are used in the measurements. The measurement shows the time it takes for a switching voltage to traverse its full range of amplitude, from full on to full off or vice versa. Often, a 10% to 90% portion of the swing is used. Slew rate is the rate, in volts or amps per second at which a signal changes amplitude. Units are voltage or current and time. Slew rate can be measured of the full swing of the signal, or just a portion of that.
The audio signal slew rate of a class D amplifier is (essentially) decoupled from the switching speed of the output stage as discussed in the previous posts. The effective signal slew rate is determined by the bandwidth of the output filter, not the switching speed of the output devices, in a class D amplifier.
I agree.
In my post, I stated that, regarding "electronic speed", what matter, in class D, is switching speed.
This has nothing to do with slew rate and doesn't impact signal integrity, but power performance.

Yes the effective signal slew rate is determined by the bandwidth of output filter, but it can be limited also by the power source and its ability to feed changing current.
If power supply is made of only linear elements, that depends on the PS impedance. But if it is an active device, there are other factors to consider.
Usually output capacitor helps to limit the output recovery time on transient load and feeding current, and you can see the PS limitations as small voltage dip or overshoot (while overshoot roughly doesn't impact signal integrity, a 'deep' dip can cause clipping).
If I have to design a PS for an audio amplifier, I'll consider a current slew rate test vs output voltage, besides the standard time recovery on transient.

I agree.
In my post, I stated that, regarding "electronic speed", what matter, in class D, is switching speed.
This has nothing to do with slew rate and doesn't impact signal integrity, but power performance.

Yes the effective signal slew rate is determined by the bandwidth of output filter, but it can be limited also by the power source and its ability to feed changing current.
If power supply is made of only linear elements, that depends on the PS impedance. But if it is an active device, there are other factors to consider.
Usually output capacitor helps to limit the output recovery time on transient load and feeding current, and you can see the PS limitations as small voltage dip or overshoot (while overshoot roughly doesn't impact signal integrity, a 'deep' dip can cause clipping).
If I have to design a PS for an audio amplifier, I'll consider a current slew rate test vs output voltage, besides the standard time recovery on transient.
OK. This thread is focused just on slew rate, so I was a bit confused by your comment, sorry.

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