From: lipp@mtu.edu (JOHN I LIPP)
Newsgroups: rec.audio.high-end
Subject: Amplifier Slew rate
Date: Wed, 16 Dec 1992 18:35:14 GMT
Organization: Michigan Technological University
NNTP-Posting-Host: 129.89.7.4
Originator: tjk@csd4.csd.uwm.edu

>In article <1g7j10INN1fm@uwm.edu>, gfl@herahera.cc.bellcore.com
>(lenahan,grant f) writes:
>|> Anything under 20 V/uS for power amps is terrible.
>|> 
>|> 4.4 v/uS is fine for a preamp, since 2.2 V rms is typical
>|> maximum Vout.
>|> 
>|> Grant
>
>How comes that slew rate < 20 V/sec is terrible ? My NAD 2155, rated at
>55 W(RMS) is specified to have a slew rate of 5.5 V/sec. It doesn't
>sound terrible at all!
>You''l also rarely find a tube amp with that slew rate.
>
>Malte


Slew rate is a large signal amplifier specification.  Most simply described, it
is the maximum voltage change per unit of time.  The reason it is important is
that as the frequency of signals go up, so does the slew rate necessary for an
amplifier to be able to keep up i.e. not distort the signal.

In mathematical terms, the slew rate is defined as dV/dt.  For a sine wave the
maximum of this is

  slew rate = V(max) * 2*pi*f

which can be converted to

  slew rate = sqrt(2)*V(rms) * 2*pi*f

or

  slew rate = sqrt(2*R*P) * 2*pi*f

where

  f		(highest) frequency of interest
  V(max)	peak (half the peak-to-peak) voltage level
  V(rms)	RMS voltage level (a CD player has a maximum output of 2 Vrms)
  R		resistance of amplifier load that it is being rated at
  P		power rating of amplifier at a given load

  pi		3.14159...
  sqrt		square-root mathematical function

The first two equations are good for signal-level devices and the last for
amplifiers.

Keep in mind that slew rate is a large signal (full power) specification.  Non-
ideal and non-linear characteristics of an amplifier often determine its value.
It is most often quoted as the _power bandwidth_.  By moving terms around from
the last equation above you get an expression for power bandwidth as

                          slew rate 
  power bandwidth = ----------------------
                     2*pi*f * sqrt(2*R*P)

Amplifiers also usually carry a frequency response specification which often
exceeds the power bandwidth specification by quite a bit.  The reason for this
is that the frequency response is a small signal (much much less than full
power) spec.  Looking at the power bandwidth equation above, you can see that
if you reduced the power rating, the bandwidth goes up.  The limit to this (the
point where reducing power output does not increase the highest allowed freq-
uency of operation) is the frequency response spec.  It is not possible for the
power bandwidth to exceed frequency response.

So, what slew rate does a 100 W/ch amplifier need to produce full power at
20 kHz?  Assuming an 8 ohm load for the 100 W rating, the answer is 5,030,000
volts/second (or more conventionally 5.03 volts/micro-second).  If you want
a margin of safety in your design (say 100 kHz at full power) then this jumps
the slew rate requirement to 25.1 volts/micro-second.

How about op-amps?  If you want an op-amp to be able to operate at a 10 volt
maximum output (assuming +/- 15 volt supplies) up to 100 kHz, the required
slew rate is 6.3 volts/micro-second.  Most op-amps, even inexpensive ones, are
able to acheive this.

Their are several reasons that an amplifier is "over-designed" in the slew rate
specification over what might appear to be necessary.  The first is that most
amplifiers have some extra headroom i.e. they can produce more power for a 
short time period than their rating.  A head room of 3 dB means twice the power
and consequently 1.414 more required slew rate.

Another is what causes the slew rate to exist.  Most transistor amplifiers are
biased internal with constant current sources.  One of these sources usually
has the job of charging a feedback capacitor that makes the amplifier stable.
Because the value of the current source that charges the capacitor is fixed, 
the voltage accross it can only change so fast and consequently the amplifier
output can change only so fast also.  Moreover, this current source is also
biasing some transistors.  If most of this current is being used to charge a
capacitor, it is not available to properly bias the transistors. The effect is
operation (and sound quality) changes in the amplifer.

Tube amplifiers tend to have low slew rates.  The reason for this is not that
tubes are poor quality devices, but that the output has to go through an output
transformer.  The transformer is basically two BIG coupled inductors, and
inductors resist high speed (high frequency) changes in current.  As a result,
the frequency limit of a tube amplifier is (usually) set by the capabilities
of its output transformer.  Most often it is not designed to exceed 20 kHz by a
large margin.  The net result is that the slew rates of tube amplifiers reflect
their small signal responses which "pale" in comparison to even modest trans-
istor amplifiers.

Their are also reasons that an over-designed slew rate won't make a difference.
Consider a stereo setup with no bi-amping.  About half the music power spectrum
is below 100 Hz for average music.  Thus, say above 5 kHz, you will probably
never use more than a tenth of the output power capability of the amplifer.
As a result, you only need 31.6% of the slew rate you thought you did. And even
if you bi-amp a system, you are likely using a less powerful amplifier on the
high-frequency part of the system.  Lower power means less slew rate is needed.

Sorry if this response was long, but I tried to make it complete as possible.

/***************************************************************************\
*  John Lipp   *  Loudspeaker design pseudo-expert and software developer   *
* lipp@mtu.edu * (Working on amplifier and surround-sound psuedo-expertise) *
\***************************************************************************/