How to calculate gain?

lumanauw · 28th July 2007, 05:36 AM

The gain is determined by a bridge of R1-R4 that is intentionally unbalanced by R5.

How come the gain becomes 30X? How to calculate the gain for this "intentionally unbalanced R1-R4 bridge"?

Jan Dupont · 28th July 2007, 06:36 AM

R2 and R3 are shorted at lower frequencies, so the resulting impedance is R2/R3 = 1K

Same goes for R4 and R5 (but for all frequencies), so R4/R5 = 909R

Makes the calculation a bit easier

lumanauw · 28th July 2007, 06:51 AM

Hi, ACD,

I still don't understand this. To get gain 30x there should be a resistor about 29k or 30k value somewhere in the network.
But in here, all the resistors are only 2k and 1k, how come the gain becomes 30x?

Jan Dupont · 28th July 2007, 07:08 AM

Just notised a mistake

R2 and R3 doesn't get shorted as R2 is connected to - Input and R3 to + Input...

Sorry for the confusion

AndrewT · 28th July 2007, 08:50 AM

Hi,
I can't see it either.
Stick the front end numbers in a sim and see what it spits out.

lumanauw · 28th July 2007, 09:22 AM

The key is "balanced bridge" of 4 resistors. And the references for 2 of them is to output node. But how to calculate gain?

lumanauw · 28th July 2007, 04:18 PM

How to merge this 2 equations, so the result is Vout/Vin in terms of R1,R2 and R3?

sawreyrw · 28th July 2007, 04:25 PM

The gain can be determined by solving the circuit equations. Neglect the effects of L1 and R13, and assume an ideal op amp.
The equations are:

(Vin-Vplus)/R1 = (Vplus-Vout)/R2

Vplus=Vout*Rp/(Rp+R3)

Where Vplus is the voltage at the op amp input terminals. (For an ideal op amp the voltages are the same at both input terminals.) Rp is the parallel combination of R4 and R5.

Solving the above equations gives:

Vout/Vin=R2*(Rp+R3)/(Rp*R2-R1*R3)

The gain for this circuit is 32.

jcx · 28th July 2007, 04:34 PM

how about the usual way? - do the voltage divider algebra with the ideal op amp assumption that the opamp +,- inputs are held exactly equal by the loop gain

lumanauw · 29th July 2007, 12:32 AM

Hi, Sawreyrw,

Thanks for the equation

One dumb question, the gain has (-) sign infront of it, is this circuit is an inverting amplifier?

28th July 2007, 06:36 AM	#2
Jan Dupont diyAudio Member Join Date: Apr 2003 Location: Copenhagen, Denmark	R2 and R3 are shorted at lower frequencies, so the resulting impedance is R2/R3 = 1K Same goes for R4 and R5 (but for all frequencies), so R4/R5 = 909R Makes the calculation a bit easier __________________ Free Schematic and Service Manual downloads www.audio-circuit.dk, Company: www.dupont-audio.com, Joint venture: www.DupontMantra.com

28th July 2007, 07:08 AM	#4
Jan Dupont diyAudio Member Join Date: Apr 2003 Location: Copenhagen, Denmark	Just notised a mistake R2 and R3 doesn't get shorted as R2 is connected to - Input and R3 to + Input... Sorry for the confusion __________________ Free Schematic and Service Manual downloads www.audio-circuit.dk, Company: www.dupont-audio.com, Joint venture: www.DupontMantra.com

28th July 2007, 08:50 AM	#5
AndrewT diyAudio Member Join Date: Jul 2004 Location: Scottish Borders	Hi, I can't see it either. Stick the front end numbers in a sim and see what it spits out. __________________ regards Andrew T.

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28th July 2007, 06:51 AM	#3
lumanauw diyAudio Moderator Emeritus Join Date: Oct 2002 Location: Bandung	Hi, ACD, I still don't understand this. To get gain 30x there should be a resistor about 29k or 30k value somewhere in the network. But in here, all the resistors are only 2k and 1k, how come the gain becomes 30x?

28th July 2007, 09:22 AM	#6
lumanauw diyAudio Moderator Emeritus Join Date: Oct 2002 Location: Bandung	The key is "balanced bridge" of 4 resistors. And the references for 2 of them is to output node. But how to calculate gain?

28th July 2007, 04:25 PM	#8
sawreyrw diyAudio Member Join Date: Apr 2006 Location: Minnesota	The gain can be determined by solving the circuit equations. Neglect the effects of L1 and R13, and assume an ideal op amp. The equations are: (Vin-Vplus)/R1 = (Vplus-Vout)/R2 Vplus=VoutRp/(Rp+R3) Where Vplus is the voltage at the op amp input terminals. (For an ideal op amp the voltages are the same at both input terminals.) Rp is the parallel combination of R4 and R5. Solving the above equations gives: Vout/Vin=R2(Rp+R3)/(RpR2-R1R3) The gain for this circuit is 32.

28th July 2007, 04:34 PM	#9
jcx diyAudio Member Join Date: Feb 2003 Location: ..	how about the usual way? - do the voltage divider algebra with the ideal op amp assumption that the opamp +,- inputs are held exactly equal by the loop gain

29th July 2007, 12:32 AM	#10
lumanauw diyAudio Moderator Emeritus Join Date: Oct 2002 Location: Bandung	Hi, Sawreyrw, Thanks for the equation One dumb question, the gain has (-) sign infront of it, is this circuit is an inverting amplifier?

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