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Author Topic: Limiter math  (Read 2602 times)

Terry Fryar

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Limiter math
« on: February 22, 2012, 01:46:18 pm »

Ok, been studying a little over the winter and brushing back up on limiter math.  This example will center around a crest 7200 amp.  I realize many variables are present such as varying speaker impedance over freq, power compression, amp limiter variation, heat, HF versus LF, etc....but let's assume some simple fixed things just for the example discussion, shall we? 
Please do note I have 6 specific questions to address scattered throughout the post:

From crest's 7200 datasheet:  output is 1000w@4ohms, input sensitivity is 1.58v (x40) at 4ohms, output voltage RMS 75v, fixed gain of x40(32db)

Our equations:

For sine wave, 1.414 more volts required to match dc power level
V = sqrt(Power*Resistance)
gain(dBu) = 20*log(v/.775)
limit(dBu) = spkrgain - ampgain

Ok, so assuming a test speaker of 1000w @ 4 ohms, the tried and true limiter math goes like this:

V = sqrt(1000 * 4) = 63v
sprkgain = 20 * log(63/.775) = 38 dBu
limit = 38 - 32 = 6 dBu

So, in my limiter I use 6 dBu for my RMS limiter, and probably add 3 or 6 db for a peak limit, depending on my knowledge of the speaker and my comfort level. 

[Question 1]:  I assume the above limiter calc is still correct??

[Question 2]:  Since I picked a test speaker right at the amp's max output, I assume my limiter's peak limits are somewhat irrelevant since the amp is already at max output?  I assume peaks should
clip the amp, since my limiter's peak stop is 3 or 6 db higher than the amp's approx max output? 

[Question 2A]: Using the above results, the obvious thing here is that I really have very little headroom, if the speaker's rms rating is the same as the amp's output, yes? 

Now.....I set up a test bench with a 7200 amp, my tek scope, a fluke 87, and a signal gen.  I injected a sine wave directly into the amp and measured amp input/output using the fluke.  Amp had no load.

[Question 3]:  The amp would clip around 2v input.  This is higher than the 1.58 sensitivity....why is this??  I assume the sensitivity is given in RMS??  Does the sensitivity change related to the amp load?  Wait...I think I measured this on the
oscope...crap...that would have been 2v peak....which would put me around the 1.5v rms....I'll have to go back and measure with the fluke to see....

[Question 4]:  The amp at clip was putting out around 78v.  I assume this is the "output voltage RMS" of 75v given in the spec sheet.  What is this value in the sheet?  Is it the maximum rms output voltage??

[Question 5]:  If the math we did above gives me 63v for my "test speaker", which is also the max output of the amp....why do I measure almost 80v in my clip test??  Shouldn't the voltage for 1000w@4ohms match the measured max output voltage of the amp??  Shouldn't that amp start clipping at 63v??  Or, if it had a 4 ohm load would it clip at 63v then??

[Question 6]:  I assume the calculated speaker voltage above of 63v is *rms*??  So if using a sine wave, I'm looking for no more than 63v out of the amp when using an rms VOM...correct?  If I had the ability to capture the wave
and measure the peaks, it would actually be at +-89v for a brief moment, correct??

Sorry for all the questions...just trying to make the math add up to the crest datasheet!

Thanks!
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Marty McCann

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Re: Limiter math
« Reply #1 on: February 22, 2012, 02:54:08 pm »

Ok, been studying a little over the winter and brushing back up on limiter math.  This example will center around a crest 7200 amp.  I realize many variables are present such as varying speaker impedance over freq, power compression, amp limiter variation, heat, HF versus LF, etc....but let's assume some simple fixed things just for the example discussion, shall we? 
Please do note I have 6 specific questions to address scattered throughout the post:

From crest's 7200 datasheet:  output is 1000w@4ohms, input sensitivity is 1.58v (x40) at 4ohms, output voltage RMS 75v, fixed gain of x40(32db)

Our equations:

For sine wave, 1.414 more volts required to match dc power level
V = sqrt(Power*Resistance)
gain(dBu) = 20*log(v/.775)
limit(dBu) = spkrgain - ampgain

Ok, so assuming a test speaker of 1000w @ 4 ohms, the tried and true limiter math goes like this:

V = sqrt(1000 * 4) = 63v
sprkgain = 20 * log(63/.775) = 38 dBu
limit = 38 - 32 = 6 dBu

So, in my limiter I use 6 dBu for my RMS limiter, and probably add 3 or 6 db for a peak limit, depending on my knowledge of the speaker and my comfort level. 

[Question 1]:  I assume the above limiter calc is still correct??

[Question 2]:  Since I picked a test speaker right at the amp's max output, I assume my limiter's peak limits are somewhat irrelevant since the amp is already at max output?  I assume peaks should
clip the amp, since my limiter's peak stop is 3 or 6 db higher than the amp's approx max output? 

[Question 2A]: Using the above results, the obvious thing here is that I really have very little headroom, if the speaker's rms rating is the same as the amp's output, yes? 

Now.....I set up a test bench with a 7200 amp, my tek scope, a fluke 87, and a signal gen.  I injected a sine wave directly into the amp and measured amp input/output using the fluke.  Amp had no load.

[Question 3]:  The amp would clip around 2v input.  This is higher than the 1.58 sensitivity....why is this??  I assume the sensitivity is given in RMS??  Does the sensitivity change related to the amp load?  Wait...I think I measured this on the
oscope...crap...that would have been 2v peak....which would put me around the 1.5v rms....I'll have to go back and measure with the fluke to see....

[Question 4]:  The amp at clip was putting out around 78v.  I assume this is the "output voltage RMS" of 75v given in the spec sheet.  What is this value in the sheet?  Is it the maximum rms output voltage??

[Question 5]:  If the math we did above gives me 63v for my "test speaker", which is also the max output of the amp....why do I measure almost 80v in my clip test??  Shouldn't the voltage for 1000w@4ohms match the measured max output voltage of the amp??  Shouldn't that amp start clipping at 63v??  Or, if it had a 4 ohm load would it clip at 63v then??

[Question 6]:  I assume the calculated speaker voltage above of 63v is *rms*??  So if using a sine wave, I'm looking for no more than 63v out of the amp when using an rms VOM...correct?  If I had the ability to capture the wave
and measure the peaks, it would actually be at +-89v for a brief moment, correct??

Sorry for all the questions...just trying to make the math add up to the crest datasheet!

Thanks!

Do not have time to answer all of your questions.

Consider two things:

1)  The input sensitivity to reach full rated output varies with the load impedance.

Also, the open circuit voltage rails will be higher with most analog amplifiers.

As you add a lower and lower load impedance the rails will drop.  You can check this on your scope with a bank of dummy load resistors of 8, 4, & 2 Ohms.

2)  Best calculation for true RMS detection is done using the minimum impedance of the transducer connected.

Happy measurements.
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Terry Fryar

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Re: Limiter math
« Reply #2 on: February 23, 2012, 09:48:25 pm »

As Marty has succinctly and correctly addressed all my questions with two comments, I'll simply follow up with more measurement reports and a few conclusions.  His two comments are in fact the root to all my questions, and after measuring I can say:  yes...the input sensitivity does in fact vary with output load, and the voltage does vary with load.  Obvious, I know!

I made a dummy load from 3 stove elements (around 8.3 ohms) and measured the 7200 with a 1k sine wave.  By the spec sheet of 590w @ 8 ohms...doing our limiter math, it should put out around 69 volts right before clip.  I measured right at 70v, with around 1.75v input.  Since I had the amp at x40 gain, we are right smack on the money (1.75x40=70)!!

Remeasuring at different loads does yield differing input/output values at clip.  However, given the differing power outputs, with current and voltage being directly related (E = IR)...I am simply verifying what we already know!  I know this is probably old and boring stuff, but I do enjoy verifying what we know against the bench now and then...it's quite reassuring I guess!

I also entered some calculated limiter numbers into a dolby lake, and measured the amplifer output voltage against several test signals/scenarios.....maybe 1 dBu off here and there, but pretty darn close to what the math said!

So, to answer my own questions in case it might be useful for someone:

1.  yes
2.  yes, given some crest factor assumptions
3.  with no load, the voltage is higher...at the spec's 4 ohm load...it would measure right
4.  yes
5.  the measured voltage will change with the load, so yes at 4 ohms, it would be 63v
6.  yes

PS:  Thanks Marty!!  You are da bomb!

« Last Edit: February 23, 2012, 09:50:05 pm by Terry Fryar »
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Nick Hickman

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Re: Limiter math
« Reply #3 on: February 25, 2012, 08:49:31 pm »

Hi Terry,

You're pretty much right on all counts.  Just to add a bit more detail ...

gain(dBu) = 20*log(v/.775)
...
sprkgain = 20 * log(63/.775) = 38 dBu

That's not a gain; it's the maximum RMS voltage to which you want to subject the speaker, expressed in dBu.

Quote
So, in my limiter I use 6 dBu for my RMS limiter, and probably add 3 or 6 db for a peak limit, depending on my knowledge of the speaker and my comfort level.

I'd consider subtracting a dB or three for the RMS limiter threshold (because the speaker's rating is on the limit of its capabilities, and power compression will rob output at these levels anyway).  And, yes, probably add 6dB for the peak limit (because the AES or IEC testing procedure guarantees that this peak voltage was used during the power test).

Quote
[Question 1]:  I assume the above limiter calc is still correct??

Other than the confusion between gain and voltage, yes.

Quote
[Question 2]:  Since I picked a test speaker right at the amp's max output, I assume my limiter's peak limits are somewhat irrelevant since the amp is already at max output?  I assume peaks should clip the amp, since my limiter's peak stop is 3 or 6 db higher than the amp's approx max output?

Remember the amplifier's peak output is 3dB above its rated power because of the crest factor of the test sine wave.  But yes, the amplifier will clip before the peak limiter is triggered.

Quote
[Question 2A]: Using the above results, the obvious thing here is that I really have very little headroom, if the speaker's rms rating is the same as the amp's output, yes?

If the SPL you need requires that you hit the limiter and your program material has a crest factor of more than 3dB (plus a bit, depending on the amplifier's "dynamic headroom", i.e. short-term ability to reproduce peaks larger than power rating + 3dB) then, yes, the result will be clipped.

Quote
[Question 3]:  The amp would clip around 2v input.  This is higher than the 1.58 sensitivity....why is this??  I assume the sensitivity is given in RMS??  Does the sensitivity change related to the amp load?  Wait...I think I measured this on the
oscope...crap...that would have been 2v peak....which would put me around the 1.5v rms....I'll have to go back and measure with the fluke to see....

Yes, the sensitivity specification is RMS and varies with load.  Crudely, at high load impedances, the amplifier's output will hit its voltage rails before it runs out of ability to deliver current whereas, at low load impedances, it will run out of current capacity before it gets near its rail voltage.  The amplifier gain is constant.

Quote
[Question 4]:  The amp at clip was putting out around 78v.  I assume this is the "output voltage RMS" of 75v given in the spec sheet.  What is this value in the sheet?  Is it the maximum rms output voltage??

On the spec sheet I have, it's labelled "Maximum output RMS voltage swing".  I'd guess it's saying that the peak output voltage is 106V.  If that's correct and applied at 4ohms, it would represent 1.5dB of "dynamic headroom" above the 1000W spec, which is a lot.

Quote
[Question 5]:  If the math we did above gives me 63v for my "test speaker", which is also the max output of the amp....why do I measure almost 80v in my clip test??  Shouldn't the voltage for 1000w@4ohms match the measured max output voltage of the amp??  Shouldn't that amp start clipping at 63v??  Or, if it had a 4 ohm load would it clip at 63v then??

Yes, 63V RMS maximum output at clip at 4ohm.  At high load impedance, I'd expect up to the "maximum voltage swing", i.e. perhaps 75V RMS, 106V peak.

Quote
[Question 6]:  I assume the calculated speaker voltage above of 63v is *rms*??  So if using a sine wave, I'm looking for no more than 63v out of the amp when using an rms VOM...correct?  If I had the ability to capture the wave
and measure the peaks, it would actually be at +-89v for a brief moment, correct??

Yes, 63V RMS on an RMS voltmeter and yes, 89V peak for a sine wave.

Nick
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Re: Limiter math
« Reply #3 on: February 25, 2012, 08:49:31 pm »


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