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Pinging EEs - cap rolloff equation??

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Posted on January 14, 2012 at 19:34:44
andyr
Audiophile

Posts: 10128
Location: Melbourne
Joined: September 2, 2000
 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

 

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RE: Pinging EEs - cap rolloff equation??, posted on January 18, 2012 at 11:35:41
Tre'
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Posts: 7940
Location: So. Cal.
Joined: February 9, 2002
 Most of what other have said and.....

The 100uf cap is not bypassing the 51K resistor. It's bypassing the impedance of the Source of the JFET.

The 51k ohm resistor is part of the equation used to calculate the impedance of the Source.

The impedance of the Source of the JFET will be lower than the 51K ohms resistor.

Tre'

Have Fun and Enjoy the Music
"Still Working the Problem"

 

Thanks, Tre ..., posted on January 18, 2012 at 13:52:44
andyr
Audiophile

Posts: 10128
Location: Melbourne
Joined: September 2, 2000
 OK, you say "The 100uf cap is not bypassing the 51K resistor. It's bypassing the impedance of the Source of the JFET."

Can you explain what the difference is?

And you went on "The impedance of the Source of the JFET will be lower than the 51K ohms resistor."

So can you tell me what the equation is for calculating the impedance of the Source?

Many thanks,

Andy


 

RE: Thanks, Tre ..., posted on January 19, 2012 at 09:20:41
Tre'
Industry Professional

Posts: 7940
Location: So. Cal.
Joined: February 9, 2002
 "So can you tell me what the equation is for calculating the impedance of the Source?"

No, but I can tell you what the equation is for calculating the impedance of the cathode of a triode.

I think it directly relates but you will have to figure out how.

The "total" cathode impedance Zk is cathode resistance of the triode Zk` in parallel with cathode resistor Rk.

Triode cathode resistance is Zk`=(Rl+rp)/(mu+1)
Where mu is amplification factor and rp is anode resistance in concrete operating point. Rl is load resistance for AC, and this is anode resistor (in preamp stage) or reflected primary load of the OPT (Za) in output stage. Note that actual Rl can be Ra//Rg, or anode resistor in parallel with second stage grid resistor.
The final formula for Zk (Zk`//Rk) is:

Zk = (rp + Rl) / ((mu + 1 + (rp + Rl)/Rk)

And our capacitor for chosen -3dB frequency is:
Ck = 1 / (2Pi * f * Zk)




Tre'


Have Fun and Enjoy the Music
"Still Working the Problem"

 

A cigar is due!, posted on January 16, 2012 at 15:47:21
clifff
Audiophile

Posts: 1741
Location: English Riviera
Joined: May 22, 2003
 I think all your points are correct.

The last one, Q3, is just a matter of judgement. But I agree, such a low turnover frequency is a complete waste of time! 1uF, 3Hz, would be fine.

Often these things are not always fully engineered (calculated). Maybe there was a 100uF on the bench and that is what (s)he used ...

 

"Often these things are not always fully engineered (calculated)." ..., posted on January 16, 2012 at 23:56:39
andyr
Audiophile

Posts: 10128
Location: Melbourne
Joined: September 2, 2000
 Thanks for confirming the equation was right, clifff. I'm think of using a value that will deliver 1uF with whatever Rsource I have. :-))

So WTF is the "English Riviera"? I'm presuming the South coast near Brighton? :-)) (I was at Sussex Uni from 1970-73.)

Regards,

Andy

 

And sometimes they are, posted on January 17, 2012 at 20:45:44
Jon Risch
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Contributor
  Since: March 1, 1999
 The value of a coupling cap does seem to be a straight forward kind of calculation, and on first glance, seems simple enough: get the LF corner down to the bottom of the audio band (or just below), and all is well.

However, upon further thought, it is NOT that simple.

1st, the phase shift at the -3 dB point is now at 45 degrees off of the original signal, and this tends to smear the time domain somewhat.

Most equipment has more than one coupling cap. If it has ten coupling caps with a - 3 dB point at a nice low 5 Hz, it will be approx. -30 dB down at 5 Hz, -10 dB down at 10 Hz, and -3.3 dB at 20 Hz.

Most recording equipment has WAY too many coupling caps in them, and not all of them are set that low. Some might be multi-pole filters that RING.
So the playback equipment must minimize any further roll-oof and associated phase shift.

So giving yourself some extra lee-way is just a smart thing to do.

Finally, most of the ill things attributed to coupling capacitors in terms of capacitor dielectric aberrations and distortions happen when the capacitor is being almost fully discharged and charged up, that is, operation below the cut-off frequency. If you make the cut-off frequency extremely low, you minimize this aspect of the capacitor distortion.

Realize that for vinyl LP playback, the fundamental record warp frequency is 0.55 Hz, and any coupling cap LF roll-off's must be well below this frequency in order to minimize the above aspect I just mentioned.

Live sound has near DC transients in the form of mic thumps, stage footfalls, etc.

Not so simple any more........
Jon Risch

 

RE: And sometimes they are, posted on January 19, 2012 at 09:29:55
Tre'
Industry Professional

Posts: 7940
Location: So. Cal.
Joined: February 9, 2002
 Jon, I think you have made very important points but, I believe, you should have prefaced them with my point above.

The bypass cap is not bypassing the Source resistor value alone but the Source resistor value in parallel with the Source impedance.

Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"

 

Thank you, Jon - a very interesting take ..., posted on January 17, 2012 at 23:24:43
andyr
Audiophile

Posts: 10128
Location: Melbourne
Joined: September 2, 2000
 It's actually not a 'standard' in-series coupling cap ... it's a bypass cap across the Source resistor of a JFET gain stage, in a phono stage. The original circuit had this (for reasons that I can't imagine) set to 51K - with a cap value of 100uF.

In my investigations into the circuit (with the aim of making the phono stage sound better), I determined that about 10K gave a better current through the JFET and I was interested to know whether the cap value could be decreased.

So now I will not lower it as much as I was thinking of doing! :-))

Regards,

Andy

 

RE: "Often these things are not always fully engineered (calculated)." ..., posted on January 17, 2012 at 09:56:06
clifff
Audiophile

Posts: 1741
Location: English Riviera
Joined: May 22, 2003
 Bournemouth (Wimborne actually), mate. I can see a palm tree from my window.

Brighton is well east and for London refugees. Don't go there!

;-)

Cliff

 

Hah! ;-)) ..., posted on January 17, 2012 at 11:22:35
andyr
Audiophile

Posts: 10128
Location: Melbourne
Joined: September 2, 2000
 Never went to Bornemuff.

Regards,

Andy

 

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