Tube data sheets give BIAS voltages at industry-standard 250Vp and 250Vs and a few other select voltages, which, unfortunately, seldom coincide with real world values, meaning we have to find some other way of estimating a prioria (in advance) what the BIAS voltage should roughly be...necessary information for both self-biased and fixed bias circuits.
Below are two slightly different methods for estimating control-grid BIAS voltage, using the tube’s published data sheet parameters:
1) Transconductance (gm) – Using desired idle plate current (Ip), idle screen (Vs) and plate (Vp) voltages and tube transconductance (gm), and tube amplification factors (mu1(triode) and mu2(pentode)):
Vg(dc) ≈ %*((3/2)*(Ip/gm)) – (Vs/mu1 + Vp/mu2)...where % ≈ 0.90-0.95
2) Perveance (G) – Using desired idle cathode current (Ik), idle screen (Vs) and plate (Vp) voltages and tube perveance (G), and tube amplification factors (mu1(triode) and mu2(pentode)):
Vg(dc) ≈ (Ik/G)^(2/3) – (Vs/mu1 + Vp/mu2)
Tube perveance (G) is not directly stated in data sheets so it must be determined *from* other data sheet information and is easily backsolved from the tube’s example triode operation data using the “Child-Langmuir 3/2’s Law” equation for triodes:
Ip = G*(Vg(dc) + Vs/mu1)^(3/2)
G = Ip/ (Vg(dc) + Vs/mu1)^(3/2)
Because this perveance value is for triode operation, where screen is connected to plate, it must be reduced slightly for pentode operation(*):
G(pentode) ≈ %*G(triode) ...where % ≈ 0.88-0.90.
Now, using either of these equations enables you to reasonably estimate the idle BIAS voltage for ANY combination of screen and plate voltage without having to extrapolate from published curves for voltages that seldom coincide with our real world voltages. Now you don't have to build something before you have a reasonable idea of what the BIAS should be when your real world Vs and Vp voltages don't match the data sheet examples and curves.
(*) Pentode perveance value could also be directly determined from published pentode operation examples.
NOTE - Astute readers will realize that the Vp/mu2 values in ALL of the above equations can be omitted causing only moderate reduction in accuracy. And, no electrons were harmed in the generation of this text.
Below are two slightly different methods for estimating control-grid BIAS voltage, using the tube’s published data sheet parameters:
1) Transconductance (gm) – Using desired idle plate current (Ip), idle screen (Vs) and plate (Vp) voltages and tube transconductance (gm), and tube amplification factors (mu1(triode) and mu2(pentode)):
Vg(dc) ≈ %*((3/2)*(Ip/gm)) – (Vs/mu1 + Vp/mu2)...where % ≈ 0.90-0.95
2) Perveance (G) – Using desired idle cathode current (Ik), idle screen (Vs) and plate (Vp) voltages and tube perveance (G), and tube amplification factors (mu1(triode) and mu2(pentode)):
Vg(dc) ≈ (Ik/G)^(2/3) – (Vs/mu1 + Vp/mu2)
Tube perveance (G) is not directly stated in data sheets so it must be determined *from* other data sheet information and is easily backsolved from the tube’s example triode operation data using the “Child-Langmuir 3/2’s Law” equation for triodes:
Ip = G*(Vg(dc) + Vs/mu1)^(3/2)
G = Ip/ (Vg(dc) + Vs/mu1)^(3/2)
Because this perveance value is for triode operation, where screen is connected to plate, it must be reduced slightly for pentode operation(*):
G(pentode) ≈ %*G(triode) ...where % ≈ 0.88-0.90.
Now, using either of these equations enables you to reasonably estimate the idle BIAS voltage for ANY combination of screen and plate voltage without having to extrapolate from published curves for voltages that seldom coincide with our real world voltages. Now you don't have to build something before you have a reasonable idea of what the BIAS should be when your real world Vs and Vp voltages don't match the data sheet examples and curves.
(*) Pentode perveance value could also be directly determined from published pentode operation examples.
NOTE - Astute readers will realize that the Vp/mu2 values in ALL of the above equations can be omitted causing only moderate reduction in accuracy. And, no electrons were harmed in the generation of this text.
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