Blog Pages


Vacuum Tube Preamp Stage

Calculating the "AC gain" of a 12AX7 common cathode stage is a fairly straight forward process. Follow along as I go through hand calculations, SPICE simulation and real world testing.


The signal generator is on the left, the high voltage power supply is in the center, and the oscilloscope is on the right. The circuit was built on an electronics breadboard using a 12AX7 vacuum tube breadboard adapter.


This is the common cathode 12AX7 gain stage we will be building. It is a common design found in some popular amplifiers. The plate resistor is 100k ohms and the cathode resistor is 1k ohms. The predicted SPICE simulation is show as well.

This stage is "inverting" which means the output will be 180 degrees out-of-phase with the input at mid-band frequencies. The SPICE simulation plot shows the out-of-phase signals. SPICE predicts the output will be about 3.6 Vpk for a 100 mVpk input signal. This is a gain of 36 V/V.


You should always begin your designs with hand calculations. It is a good way to check your understanding of the circuit you are trying to build.

The equation in the top left is what you will use to calculate the gain of an "unbypassed" common cathode gain stage. If your cathode resistor is bypassed with a capacitor, you can remove the Rk(u+1) from the calculation and get much higher stage gain. Note: I have omitted the "minus" sign that indicates "phase inversion".


 The gain equation we are using is based on the following assumptions:
1. All tube parameters are held constant
2. The signals being amplified are small
3. We somehow know the value of internal AC plate resistance "rp"
4. We somehow know the value of the tubes amplification factor "u" mu

I will show you how to get the values for "rp", "u" and "gm" in a future post.
For now, let's assume u = 82 and rp = 40k ohms. We don't need "gm" for this exercise.


The circuit was built on a breadboard using the resistor values shown in the schematic. The resistors are simply connected to the appropriate tube section with the header pins that are identified on the PCB. Heater connections 4, 5, and 9 are the center three pins. These adapters are designed for dual triodes so the second tube section is connected to the three pins on the right.


Simulation is one thing. But, reality is what really matters. According to my hand calculations the voltage gain should be about 36.7 volts per volt. That means if we put a 0.1 Vpk signal into this stage we should get an output signal around 3.67 Vpk.

 The blue trace in the image is the 0.1 Vpk input signal. The yellow trace is the output signal which measures right around 3.6 Vpk. Not bad! Notice that the signals are out-of-phase.


SPICE predicted the DC plate voltage would be around 151.43 VDC. The acutal Plate votlage measured was 150.5 VDC. Again, not bad at all.



SPICE predicted the DC cathode voltage would be around 0.985 VDC. The actual cathode votlage measured was 1.112 VDC. Again, pretty close.


If you are really interested in tube audio design here are some books I recommend.

1. Radiotron Designer's handbook by RCA - Totally old and totally awesome.
2. Audio Cyclopedia - Expensive but worth it.
3. Beginner's Guide to Tube Audio Design - Not for "beginners" but a handy reference for equations

Thanks for reading,

No comments:

Post a Comment