Updated Tube Comparison Table

[HotBluePlates]

On another forum a table of the data sheet values for various tube types was assembled as an aid for estimating the relative performance of the tubes listed.  While handy, these tables had a shortcoming: If I swap a 12A_7 into a guitar amp socket originally calling for a 12AX7, it won't realize the "data sheet values." Assumptions based on these values will then be wrong. To remedy this I have put together a table that shows, "What happens when I plug _____ into a 12AX7's socket?"

Scenario/Assumptions:

• Subject Tube is in a common-cathode circuit fed from a 300v supply, with a 100kΩ plate load and a bypassed 1.5kΩ cathode resistor.
• Subject Tube is in the input stage of a Fender-style amp, fed from the #1 Input Jack.

     -  There are two 68kΩ resistors in parallel due to Fender's switching arrangement, for 34kΩ in series with a pickup assumed to be 7kΩ.
     -  The above is in parallel with a 1MΩ grid leak resistor, and Input+Miller Capacitance of the Subject Tube.
     -  No extra-capacitance was added to account for a guitar cable, etc.
   

• Subject Tube has a "big enough" coupling capacitor (we're not considering any impact due to bass roll-off).
• Subject Tube is followed by a 12AX7

     -  The 12AX7 has a 1MΩ grid-leak resistance (or volume control at maximum)
     -  The 12AX7 also has a 300v supply, 100kΩ plate load, and bypassed 1.5kΩ cathode resistor; it develops a gain of 62 while having data-sheet capacitances.

The 100kΩ plate load and 1.5kΩ cathode resistor were chosen because they are near-ubiquitous in Fender-style preamps and other guitar amps. The 300v supply was chosen because it is near-enough to common preamp supply voltages, and rounds up a little to give low-Mu tubes a fighting chance.

Beyond simply noting the tube's Amplification Factor ("Mu"), Internal Plate Resistance ("rp") and Transconductance ("Gm"), a few other key figures are displayed. These include the tube stage's output impedance, and the treble roll-off frequency at the tube's output that results from this impedance, and the next stage's input capacitance. "Input -3dB" also shows the tube's roll-off in its input circuit due to its own Miller Capacitance.

[HotBluePlates]

Below is the Tube Comparison Table, followed by a definition of each column:

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.​

[HotBluePlates]

How were the different values determined? Well, from the data sheets! In particular, I used a graphical method outlined by York (Chapter 3), and shown in various places in RDH4.

Method:

A d.c. loadline for 100kΩ was plotted (Red line) on each tube's characteristic curves along with a line (Green line) for the 1.5kΩ cathode resistor. The crossing of these lines indicates the D.C. Operating Point of plate voltage and plate current.

Where characteristic curves were available, a vertical was erected at the plate current of the D.C. Operating Point, and values of Mu, Gm (transconductance), and rp (internal plate resistance) were read directly.

Where characteristic curves were not available, rp was found by plotting a tangent to the "grid bias curve" at the D.C. Operating Point (Orange line). In most cases, an actual curve was not present, and the line is tangent to the nearest actual grid bias curve.

Mu was graphically calculated by laying out approximately equal-changes of grid voltage while keeping plate current fixed (a horizontal Purple line) and noting the corresponding change of plate voltage. ∆ Plate Volts / ∆ Grid Volts = Mu.

Gm was graphically calculated by estimating an equal-change of grid voltage while keeping plate voltage constant (a vertical Pink line) and noting the corresponding change of plate current. ∆ Plate Current / ∆ Grid Volts = Gm.

Sometimes Mu or Gm was calculated rather than obtained graphically. Given rp and one of the other quantities, the third can be found from Mu = Gm x rp.

Given Mu, Gm and rp based on the actual D.C. Operating Point imposed by the circuit, Voltage Gain was calculated using the method demonstrated by Aiken and in RDH4.

Tube capacitances were taken from the relevant data sheet, using the "With Shield" case, if given. This seemed a good middle ground, as cable and stray wiring capacitances would erode the bandwidth of the tube (but are specific to build implementation). NOTE: while most data sheets mirror the same values of capacitance, some do not. RFT's 6SL7 claims lower capacitance than RCA's 6SL7; in this case the higher-pF values were used.

[HotBluePlates]

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:

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.

[HotBluePlates]

Inside Baseball Time: So what's wrong with the existing table? It's that we won't achieve the Gm and rp values listed when we plug the tube in an average guitar amp!

• Look at the 12AU7 line: at the far right we see Plate Current = 10.5mA. What this means is the 12AU7 must be passing 10.5mA (while also having 250v at the plate, in accordance with the condition on the right on Page 2 of the data sheet).​
• If the 12AU7 has a 100kΩ plate load resistor, how much supply voltage will the amp need? At least [(100kΩ x 10.5mA) + 250v] = 1050v + 250v = 1,300 volts!!​
• We don't have 1.3kV supplying the preamp of any guitar amplifier, so if we plug a 12AU7 in the average socket of a guitar amp, we will not get anywhere close to 10.5mA of plate current when also using a 100kΩ plate load resistor typical for a 12AX7 stage.​
• And once we have lower plate current in that 12AU7, Gm will not be as high, nor rp so low.​

Take another example of the 12AV7: the data sheet condition cited mentions a plate current of 18mA. Repeat the math above, and we need 1,950 volts in the power supply to achieve that with the 100kΩ plate load resistor.

Ditto for the 6SN7: the cited condition (right column of Page 3) would require a supply of 1,150v to get 9mA through the 100kΩ plate resistor.

{EDIT: remote image attached here --PRR}

[HotBluePlates]

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: 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.​

[HotBluePlates]

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)​

[Willabe]

Thank you HBP for doing all of this and posting it here. 

[tubeswell]

Mods - please stickie this thread

[66Strat]

The Tube Comparison Table and the tutorial on the use of tube average characteristic graphs are very helpful. Thank you HBP for the time and effort spent putting this presentation together.