Below is the Tube Comparison Table, followed by a definition of each column:
(https://i.imgur.com/eKUgKds.png)
Definitions:
Voltage Gain - Output Voltage divided by Input Voltage for this tube stage. It is the tube's realized-Mu reduced by the voltage divider action of the tube's internal plate resistance ("rp") and the external load of the plate load resistor and the next stage's grid-leak resistor.
Gain Decibels - Voltage Gain expressed in decibels; 20 log (Voltage Gain / 1)
Input -3dB - The treble roll-off at the input circuit of the tube. It is due to the tube's Miller Capacitance, and the resistance-to-ground through all parallel paths at the input.
Output -3dB - The treble roll-off at the output circuit of the tube. It is dominated by the Miller Capacitance of the next tube stage (assumed here to be a 12AX7 of typical gain), and is influenced by the Subject Tube's output impedance.
Mu - the Amplification Factor of the tube at the operating point defined by the supply voltage, plate load resistor and cathode bias resistor. For some tubes, this varies greatly from the commonly-cited data sheet Amplification Factor.
Gm - the Transconductance of the tube at the operating point defined by the supply voltage, plate load resistor and cathode bias resistor. For many tubes, this is substantially lower than commonly-cited data sheet Gm, because when tube plate current falls the Gm falls.
rp - the Internal Plate Resistance of the tube at the operating point defined by the supply voltage, plate load resistor and cathode bias resistor. For many tubes, this is higher (sometimes much higher) than commonly-cited data sheet rp, because when tube plate current falls the rp rises (dramatically so at low plate current).
Output Z - the Output Impedance of the tube at the operating point defined by the supply voltage, plate load resistor and cathode bias resistor. It is the total resistance of the tube's operating point rp, the 100kΩ plate load resistor, and the next stage's 1MΩ grid-leak resistor in parallel.
Plate Voltage - Idle plate voltage of the tube resulting from the chosen supply voltage and resistor values. It is the Supply Voltage minus the Plate Load Resistor's voltage drop.
Plate Current - Idle plate current of the tube resulting from the chosen supply voltage and resistor values. This is the amount of plate current the tube will realize based on the manufacturer's data sheet.
The graphical calculations can be inspected in the album below.
https://imgur.com/a/zfl3BRh#
The following is used as the Equivalent Circuit for the tube used to calculate the treble roll-offs, taken from RDH4 Page 494 but adds Ci and Rg to the left of the tube:
(https://i.imgur.com/6EZfPzU.png)
In RDH4, Ci and Rg on the right side of the diagram represent the grid-leak resistor and input capacitance (including Miller Capacitance) of the next tube, meaning the one after the Subject Tube. These are included in the RDH4 model to show how well the Output Impedance of the tube studied can drive capacitance hanging from its output, and therefore the treble roll-off due to the circuit following the Subject Tube's output.
My model adds Ci and Rg at the front of the studied tube. As a result, my table includes two -3dB frequencies describing treble roll-off: one at the Input Circuit to capture the Subject Tube's Input+Miller Capacitance and resistance-to-ground, and a second at the Output circuit to capture the studied tube's Output Capacitance and ability to drive the next-tube's Input+Miller Capacitance.
So what?!? How do I make use of this?
Look at my table on the far-right: Plate current for each tube lands in a range between 1.04mA and 2.25mA. Can we see a pattern here?
- The supply voltage used is 300v, so if the tube short-circuited plate-to-ground, current can only rise to 300v / 100kΩ = 3mA.
- Calculated values for each tube land in a range of 34.7% to 75% of that 3mA maximum.
- When the tube pulls 75% of the 3mA maximum, 75% of the supply voltage is dropped across the plate load resistor: 2.25mA x 100kΩ = 225v ---> 225v / 300v = 75%
- On the other side of the coin, the tube will retain at least 25% of the supply voltage just to operate.
Plate Current matters!!
Out of convenience, we routinely cite tube characteristics as though they're unchanging. Except our tubes behave differently at high current and low current.
Take the 12AY7 (https://frank.pocnet.net/sheets/135/1/12AY7.pdf): the data sheet condition claims a transconductance of 1.75mA/volt (or 1750 micromhos, or 0.00175 A/volt), with an internal plate resistance of 22.8kΩ. Mu is 22.8kΩ x 0.00175 A/volt = 39.9 (round up to the data sheet's "40").
- But that data was for a 12AY7 passing 3mA, with 250v remaining on its plate. We would need a supply of 550v to do that with our 100kΩ plate load resistor, so we don't realize the full 3mA in a typical guitar amp.
Below we have the graph of characteristics from page 4 of the 12AY7 data sheet linked earlier. We can see what happens when plate current falls from 3mA to 1mA (assume plate voltage remains constant at 150v), which are the ends of each colored curve.
- Mu falls from 45.6 to 42.8 (6% reduction)
- Gm falls from 1.88mA/volt to 1.12mA/volt (40% reduction)
- rp rises from 24kΩ to 38kΩ (58% increase)
(https://i.imgur.com/5vb8q1r.png)