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.

The output is taken from where the plates connect to the 100k plate load resistor **R _{L}**. The 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 **R _{K}**. 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

The Radiotron Designer's Handbook^{1} 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.

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

The triodes are represented by controlled voltage sources in series with plate resistances **r _{p}**. When the grid-to-cathode voltage

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:

Similarly for the right triode we get

Applying KVL to the grid circuits gives us

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

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:

Next we apply Cramer's Rule and obtain the plate currents **i _{1}** and

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

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

The minus sign indicates that this is an inverting amplifier for both channels. The term **2μR _{K}** 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

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

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

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