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13th February 2003, 03:53 PM  #1 
diyAudio Member
Join Date: Nov 2002
Location: Norway

Output impedance
Could somebody help me with this problem, I'm just wondering what the output impedance is for the circuit beneath.
I have tried to find the formula for the output impedance, but I don't know if it's correct. the formula I found is: Zout= Rk  (rp+Ra+u*Rk) or (Rk*(rp+Ra+u*Rk)) / (Rk+rp+Ra+u*Rk) 
13th February 2003, 04:53 PM  #2 
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Join Date: Jan 2003
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Zout = Rk // [(Ra+ra)/(u+1)]
To put it in words, looking up into the anode, all resistances are divided by a factor of (u+1), and that little lot is in parallel with your cathode bias resistor. The equation you quoted would imply that loading a cathode follower with a constant current sink insted of a cathode resistor would significantly increase its output resistance.
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13th February 2003, 05:41 PM  #3 
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Join Date: Nov 2002
Location: Norway

thanks
Do you have some more hints about how I can derive this formula?? I have tried a couple of times but haven't got the right answer yet 
13th February 2003, 06:04 PM  #4 
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Join Date: Aug 2002
Location: Belgium

Zo AT THE CATHODE.
Hi,
The easiest way is: Output impedance (cathode): Rk' = (Rl+ra)/(mu+1) Rout = Rk'Rk Where: Rp = the plate resistor Rl = the load resistance, or the input resistance of the next stage Ra = the total load resistance, which is Rp in parallel with the input resistance of the next stage, Rl. If there is no Rl, Ra = Rp. ra = the internal plate resistance of the tube mu = the mu of the tube Keep in mind this for a bypassed Rk. Cheers,
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13th February 2003, 06:13 PM  #6 
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Join Date: Aug 2002
Location: Belgium

Bypassed Rk?
Hi,
Meaning : cathode resistor bypassed with a capacitor. Should have clarified that. For the unbypassed common cathode circuit you can use this: Rout = [(Ra + ra)/(mu + 1) * Rk] / [(Ra + ra)/(mu + 1) + Rk] Where: Rk = the cathode resistor Ra = the total load resistance, which is Rp in parallel with the input resistance of the next stage, Rl. If there is no Rl, Ra = Rp. ra = the internal plate resistance of the tube mu = the mu of the tube Cheers,
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Frank 
13th February 2003, 06:35 PM  #7 
diyAudio Moderator

Pardon my ignorant question, but since the output is being taken from the cathode, won't bypassing the cathode result in... silence?
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13th February 2003, 06:51 PM  #8 
diyAudio Senior Member
Join Date: Aug 2002
Location: Belgium

I SEE.
Hi,
Sorry if I got anyone confused here. Output impedance (cathode): Rk' = (Rl+ra)/(mu+1) Rout = Rk'Rk Actually this is the output impedance calculated for a common cathode stage,signal is of course taken from the plate,cathode R is bypassed. Output impedance (plate): Rout = (ra * Rp)/(ra + Rp) Hope this sets it straight. Cheers,
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Frank 
13th February 2003, 07:45 PM  #9 
diyAudio Member

The complicated way, of course, would be to graph operation, determine grid drive for output, then add output voltage to input voltage as NFB, and calculating Zo based on Rp, Rl and amount of NFB applied.
No doubt those equations simplify all this into a single operation... Tim "but I like the scenic route!" 
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