[sdiy] Equation for converting V PP to dBm?

[Tim Stinchcombe]

I'm going to ignore all this...

> I've been researching how to convert a Peak to Peak Voltage 
> into dB and I've come up with 4 slightly different equations 
> which all give different answers. I've also had a few 
> different people tell me that different ones were the 'right' 
> one - so I thought I'd ask here.
> 
> 1) dB = 20*log_10(Vpp/0.707)
> 2) dB = 20*LOG10(Volts_peak_to_peak/SQRT(0.008*Z))
> 3) db = (20log10) (RMS ) & RMS= 0.707*P-P
> 4) dB = 20 log10 (Vout / Vin)

... and go straight for this:

> What I'm trying to do is plot the response curve of the 2164 
> based on the data sheet spec of -33mV/dB. I figure if I can 
> convert V PP to dB I'll also have mV to V PP.

It's a current in, current out device, so say we have Iin, Iout. So in
decibels, the gain of Iout to Iin is 20*log10(Iout/Iin). This is specified
as -30dB/volt input; call input voltage Vc. Hence:

-30 = 20*log10(Iout/Iin)/Vc, or

-3/2*Vc = log10(Iout/Iin).

Take 'to the power 10' to rid logs gives:

Iout/Iin = 10^(-3/2*Vc), or

Iout = Iin*10^(-3/2*Vc)

from which you can calculate currents, and voltages depend how you are
converting volts <-> current at input and output (and if using the 30k
resistors, as datasheet, at input and for feedback of i-v converting OA at
output, just replace Vout for Iout, Vin for Iin).

For exponential conversion, base 2 is real handy, for 'volts/octave' etc. So
say

10^x = 2, which says x = log10(2), hence

10 = 2^(1/x) = 2^(1/log10(2)), and substitute in above

Iout = Iin*(2^(1/log10(2)))^(-3/2*Vc) = Iin*2^(-3*Vc/(2*log10(2))), or
approx

Iout = Iin*2^(-5*Vc) on evaluating the constant in the exponent, which says
roughly 0.2V/octave!

(This is the same whether you are talking RMS or pk-to-pk, as the conversion
factor cancels both sides.)

(I just happened to have these calcs right in front of me, as I've been
looking at both the Doepfer DIY board, and an A-132-3, which both use this
chip!)

Tim
__________________________________________________________
Tim Stinchcombe 

Cheltenham, Glos, UK
email: tim102 at timstinchcombe.co.uk
www.timstinchcombe.co.uk