electronique - audio - amplifier vacuum tube circuits and equations

8/17/2019 Electronique - Audio - Amplifier Vacuum Tube Circuits and Equations

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Vacuum Tube Amplifier Circuits and Equations

General

Following is a collection of tube amplifier circuits and equations. It will be updated regularly as new papers on

different tube circuits and configurations are added to the website (beh ormai l’ho stampato).

Common-cathode stage, fully-bypassed cathode:

Voltage Gain:

Av = (mu * Rp!(Rp " r a

Input impedance:

Rin = Rg

Output impedance (plate):

Rout = (r a * Rp!(r a " Rp

Output impedance (cathode):

R#$ = (Ra"r a!(mu"%Rout = R#$&&R#

Input capacitance:

'in ='g# " 'gp*(Av " %

Freuency response:

f% = %!(*pi*'i*Rg ) highpass brea#point due to 'i!Rg

f = %!(*pi*'o*(Rout " Rl ) highpass brea#point due to 'o!Rout!Rl

f = %!(*pi*'#*R#$&&R# ) highpass brea#point due to '#!R#

%


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f+ = %!(*pi*Rout*'in ) lowpass brea#point due to Rout of previous stage and 'in

,here-

Rg = the grid resistorRp = the plate resistorRl = the load resistance or the input resistance of the ne/t stageRa = the total load resistance which is Rp in parallel with the input resistance of the ne/t stageRl. If there is no Rl Ra = Rp.r a = the internal plate resistance of the tube

mu = the mu of the tube'g# = the grid)to)cathode capacitance'gp = the grid)to)plate capacitanceAv = the stage voltage gain

0ote that Rl is ignored in the output impedance calcuations for the output not because it doesn$t affect output

impedance of the overall circuit but because output impedance is traditionally the impedance of the output of thatgain stage loo#ing bac# into the output. Rl is the input impedance of the following stage so it is not included. 1fcourse when calculating overall gain in an amplifier the loading effect of Rl must be ta#en into account. In the caseof the cathode impedance Rl must be included because it will affect the impedance seen loo#ing bac# into thecathode.

Common-cathode stage, unbypassed cathode:

Voltage Gain (Output !):

Av = (mu * Rp!(Rp " r a " (mu " %*R#

Input impedance:

Rin = Rg

Output impedance (Output !):

Rout = 2(r a " (mu " %*R# * Rp3 ! 2(r a " (mu " %*R# " Rp3

Output impedance (Output "):

Rout = 2(Ra " r a!(mu " % * R#3 ! 2(Ra " r a!(mu " % " R#3


3/7

Freuency response (Output !):

f% = %!(*pi*'i*Rg ) highpass brea#point due to 'i!Rg


,here-

Rg = the grid resistor

Rp = the plate resistorR# = the cathode resistor

Rl = the load resistance or the input resistance of the ne/t stageRa = the total load resistance which is Rp in parallel with the input resistance of the ne/t stageRl. If there is no Rl Ra = Rp.r a = the internal plate resistance of the tubemu = the mu of the tube

0ote that Rl is ignored in the output impedance calcuations for output % not because it doesn$t affect outputimpedance of the overall circuit but because output impedance is traditionally the impedance of the output of thatgain stage loo#ing bac# into the output. Rl is the input impedance of the following stage so it is not included. 1fcourse when calculating overall gain in an amplifier the loading effect of Rl must be ta#en into account. In the caseof the output ta#en from the cathode Rl must be included because it will affect the impedance seen loo#ing bac#

into the cathode.

#ingle-stage in$erting feedbac% amplifier:

.

Gain:

Acl = (Ro " A*Rf ! (Ri " Rf " Ro ) Ri*A

Input impedance:

Rin = (Ri * A ) Ri ) Rf ) Ro!(A)%

Output impedance:


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Rout = (Ri " Rf * 2Ro ! (Ri " Rf " Ro ) Ri*A3

Freuency response:

f% = %!(*pi*'i*Ri ) highpass brea#point due to 'i!Ri


,here-

Acl = closed loop gain

A = open loop gainRi = input resistanceRf = feedbac# resistanceRo = internal output resistance of the stage (the plate load resistor in parallel with the internal plateresistance r a of the tube plus the reactance of 'o if not negligible at the frequency of interest

0ote that for negative feedbac# A must be a negative quantity. If A is positive the feedbac# will be positive. 4he value of A can be calculated by using the equations for the common cathodeamplifier stage.

0ote that Rl is ignored in the output impedance calcuations not because it doesn$t affect outputimpedance of the overall circuit but because output impedance is traditionally the impedance ofthe output of that gain stage ) Rl is the input impedance of the following stage so it is not

included. 1f course when calculating overall gain in an amplifier the loading effect of Rl must be ta#en into account.

Global negati$e feedbac% amplifier:

+


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Gain:

Acl = A*(Ri"Rf ! (Ri " Rf " Ro " Ri*A

0ote- if Ro is assumed 5ero Acl= A ! (% " A* Ri ! (Ri " Rf

Input impedance:

Rin = Rg ! (%6 ) Acl*Ri!(Ri"Rf

0ote- If closed loop gain is high enough Rin is essentially infinite

Output impedance:

Rout = ((Ri " Rf * Ro ! (Ri " Rf " Ro " Ri*A

0ote- if Ro is assumed 5ero Rout = 7.

,here-

A = open)loop gain

Acl = closed)loop gain

A = open loop gainRi = input resistanceRf = feedbac# resistanceRo = internal output resistance

8


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0ote that for negative feedbac# A must be a positive quantity. If A is negative the feedbac# will be positive. 4he value of A can be determined by opening the loop and measuring the outputvoltage and dividing by the applied input voltage.

&hase-shift oscillator:

'inimum gain reuired for oscillation:

A(min = 9

4he value of A can be calculated by using the equations for the common cathode amplifier stage.It must be 9 or greater to sustain oscillations. A gain of e/actly 9 or :ust enough to sustainoscillations will produce the lowest distortion sine wave at the plate of the tube.

Oscillation freuency:

f o = %!(*;i*


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R$ = R*>

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