The Gretsch Chet Atkins preamp has two channels, each with its own bass and treble controls. The channels are combined in a 12AX7-based mixing circuit.

Gretsch Chet Atkins active mixer circuit

The output is taken from where the plates connect to the 100k plate load resistor RL. The cathode resistor RK is 1.5k. Since the resistors carry the plate current of two triodes, the DC operating point is the same as for a single triode with a 200k plate load resistor and 3k cathode resistor.

AC voltage gain for each channel is less than for a single triode amplifier because of additional negative feedback. Imagine a rising voltage on the left input (channel 1) and no signal on the right. The increasing grid-to-cathode voltage causes an increase in plate current through the left triode, which creates more current through the cathode resistor RK. This raises the voltage across the resistor, causing the cathode voltage to rise and counteract the rising grid-to-cathode voltage induced by the input signal. Classic negative feedback. Moreover, we have common cathode coupling: a rise in cathode voltage for the left triode creates a similar rise in cathode voltage for the right triode. The net result is that the rising input signal causes the total current through the plate load resistor RL to increase while at the same time negative feedback in both triodes causes the total current to decrease.

The Radiotron Designer's Handbook1 calls this a "common plate load mixer." Unfortunately no gain formula is mentioned for the Chet Atkins configuration, where no cathode bypass capacitor is used, so we'll derive a formula here. If you want to use the gain formula but prefer to skip the math, just scroll down to the bottom of the page.

The AC Circuit

Here is the AC circuit, where DC voltages are considered zero.

Gretsch Chet Atkins active mixer AC circuit

The triodes are represented by controlled voltage sources in series with plate resistances rp. When the grid-to-cathode voltage vg1 increases by 1 volt, for example, the voltage across the the controlled voltage source on the left increases by μ volts, where μ is the triode's amplification factor.

Voltage Gain

We apply Kirchhoff's Voltage Law (KVL) to the left triode plate circuit by taking the sum of the voltages and setting them equal to zero:

equation 1

Similarly for the right triode we get

equation 2

Applying KVL to the grid circuits gives us

equation 3

equation 4

We substitute these grid voltages into the plate circuit formulas and with a little algebraic re-arrangement the result is

equation 5

equation 6

The amplification factor μ for a high-mu triode is much greater than 1 (For the Gretsch's 12AX7, for example, μ = 100.) So these relations are very close:

equation 7

equation 8

Next we apply Cramer's Rule and obtain the plate currents i1 and i2 as a function of the input signal voltage vin.

equation 9

equation 10

According to Ohm's Law the output voltage is minus the product of the plate resistor value and the sum of the currents.

equation 11

Substituting the currents that we just computed and simplifying we get the final gain:

equation 11

The minus sign indicates that this is an inverting amplifier for both channels. The term 2μRK represents negative feedback that is absent if the cathode resistor is fully bypassed by a large capacitor. For a simple triode amplifier with an unbypassed cathode resistor, the feedback term is only (μ+1)RK. So the Gretsch common plate load mixer has approximately twice as much negative feedback.

Further Reading

1F. Langford-Smith, Ed., Radiotron Designer's Handbook, 4nd Ed., (Harrison: RCA, 1953), p. 800.

2Richard Kuehnel, Vacuum-Tube Circuit Design: Guitar Amplifier Preamps, 2nd Ed., (Seattle: Pentode Press, 2009).