Simple transfer function of circuit

[Rob119]

http://www.flickr.com/photos/61432156@N02/5593767202/

Ok so I'm trying to find the transfer function relating voltage across the 8 ohm resistor (speaker) with the input voltage for the circuit shown above...

The two op amps simply provide a gain of 3... and by simple voltage division I am getting the transfer function (Vspeaker / Vinput) to be 3*(8/(8+1/sC1)) or [24sC1/(8sC1 + 1)].

It looks to me as if C2 and R5 have no effect on the transfer function...

But my professor is asking to design C1 and C2 such that there are TWO corner frequencies (-3dB points) at 80Hz and 28kHz... how can this be possible if the output across the speaker is simply a high pass filter? Or did I calculate the transfer function wrong??

 

[berkeman]

http://www.flickr.com/photos/61432156@N02/5593767202/

Ok so I'm trying to find the transfer function relating voltage across the 8 ohm resistor (speaker) with the input voltage for the circuit shown above...

The two op amps simply provide a gain of 3... and by simple voltage division I am getting the transfer function (Vspeaker / Vinput) to be 3*(8/(8+1/sC1)) or [24sC1/(8sC1 + 1)].

It looks to me as if C2 and R5 have no effect on the transfer function...

But my professor is asking to design C1 and C2 such that there are TWO corner frequencies (-3dB points) at 80Hz and 28kHz... how can this be possible if the output across the speaker is simply a high pass filter? Or did I calculate the transfer function wrong??

There does appear to be something missing. For the C2 leg to have an effect and roll off gain at high frequencies, the preamp has to have a finite and known output impedance. Are you given datasheet info for the preamp part? If it were ideal with zero output impedance, you'd need to add your own output resistor before the C2 leg.

 

[Rob119]

interesting didnt think of that... an lm741 has ~75 ohms output impedence (typically) until after like 30 kHz when it becomes much larger.

ill see if I can redo some calculations taking that output impedance into consideration.

 

[berkeman]

They want you to drive an 8 Ohm speaker with an LM741 opamp? Not practical. Maybe you can earn bonus points on the assignment pointing that out...

 

[Rob119]

well I am just modeling the speaker with an 8 ohm resistor and taking measurements, but I will point that out. After redoing the calculations with the 75 ohm output resistance my transfer function is a mess... i don't know what to make of it.

the lab is for a class but you do it at home.. and the professor doesn't answer emails. very frustrating.

 

[berkeman]

well I am just modeling the speaker with an 8 ohm resistor and taking measurements, but I will point that out. After redoing the calculations with the 75 ohm output resistance my transfer function is a mess... i don't know what to make of it.

the lab is for a class but you do it at home.. and the professor doesn't answer emails. very frustrating.

Here's a hint that may help with the transfer function. The low-frequency and high-frequency corners are far enough apart that you may be able to treat them separately in fairly accurate approximations. Can you see any simplifications in your messy transfer function for low-frequency and high-frequency approximations?