Equation for the roll-off frequency for a resistor with parallel cap?

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andyr

I was hoping that someone could confirm my below thinking.

Background: I have seen in a JFET phono stage cicuit that the JFET has a Source resistor of 51K bypassed with a 100uF cap.

Can you confirm the following:

1. There is an equation which gives the approximate roll-off frequency, for particular values of resistor-and-parallel-cap.

I understand this equation is: f = 160,000/(uF * R)

2. So for a 51K Source res and 100uF cap bypass, this gives a corner frequency of 0.03Hz?  ( 160,000/(100*51,000) )

Q1: Is the above equation correct?

Q2: If I changed the Source res to 10K, I would need to increase the cap value to 510uF, to keep the same roll-off frequency?

Q3: Surely, a corner frequency of 0.03Hz is ridiculously low – the cap value could have been 1uF in the original situation (Rsource of 51K) for a corner frequ of 3Hz?


Thanks a lot,

Andy

JohnR

Remember that a microfarad is a millionth of a farad.

andyr

Remember that a microfarad is a millionth of a farad.

Thanks, John, I'm aware of that.

AIUI, the equation I quoted [f = 160,000 / (uF*R)] copes with that.

Regards,

Andy

JohnR

Oh right.

Speedskater

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When you add a real world phone cartridge to the mix, things get real complicated real fast!

Hagerman covers some of the math:
http://www.hagtech.com/pdf/riaa.pdf

Ethan Winer

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I have seen in a JFET phono stage cicuit that the JFET has a Source resistor of 51K bypassed with a 100uF cap.

I'd have to see the circuit to be sure, but my guess is the resistor sets the DC operating level, and the capacitor sets the gain at audio frequencies.

--Ethan

Steve

I was hoping that someone could confirm my below thinking.

Background: I have seen in a JFET phono stage cicuit that the JFET has a Source resistor of 51K bypassed with a 100uF cap.

Can you confirm the following:

1. There is an equation which gives the approximate roll-off frequency, for particular values of resistor-and-parallel-cap.

I understand this equation is: f = 160,000/(uF * R)

2. So for a 51K Source res and 100uF cap bypass, this gives a corner frequency of 0.03Hz?  ( 160,000/(100*51,000) )

Q1: Is the above equation correct?

Q2: If I changed the Source res to 10K, I would need to increase the cap value to 510uF, to keep the same roll-off frequency?

Q3: Surely, a corner frequency of 0.03Hz is ridiculously low – the cap value could have been 1uF in the original situation (Rsource of 51K) for a corner frequ of 3Hz?


Thanks a lot,

Andy

Would be good to see the schematic. The source resistor usually sets the parameters of the device. With such a high value, I am guessing that the device is DC coupled at an elevated voltage.

There is probably good reason why 100uf is used, such as prevention or at least headroom to prevent ultra low frequency oscillation. Beside that, 3hz for a corner frequency will compromise response at 20hz. Of course that depends upon your goals.

Cheers.

andyr

Thanks for the responses, guys.

I have found out the equation I posted: f = 160,000/(uF*R)  is correct.  Sure, 3hz for a corner frequency will probably compromise response at 20hz ... so I'll use 20uF to give 0.7Hz as the -6dB frequency.


Regards,

Andy

Steve

Thanks for the responses, guys.

I have found out the equation I posted: f = 160,000/(uF*R)  is correct.  Sure, 3hz for a corner frequency will probably compromise response at 20hz ... so I'll use 20uF to give 0.7Hz as the -6dB frequency.


Regards,

Andy

A cap for .7hz sounds good Andy. I mentioned it since the other components in your system also have break points and this would add to any compromise.
I would also carefully check, with a scope if possible, to make sure no low frequency oscillations, thumps occur during power on and off, indicating possible close to self oscillation. Just a precautionary suggestion with any changes in design Andy.   

Cheers and good luck.

andyr

A cap for .7hz sounds good Andy. I mentioned it since the other components in your system also have break points and this would add to any compromise.
I would also carefully check, with a scope if possible, to make sure no low frequency oscillations, thumps occur during power on and off, indicating possible close to self oscillation. Just a precautionary suggestion with any changes in design Andy.   

Cheers and good luck.

Thanks, Steve.  :)

Regards,

Andy