### Example 4.1

A 12AX7 has a plate load resistor, Rb, of 220 k ohms and the grid resistor of the following stage, Rcf, is 470 k ohms. Tube manual data on the 12AX7 gives Amplification factor = 100 and plate resistance = 80 k ohms. What is the gain of this 12AX7 amplifier

### Solution.

First we calculate Rbc.

Rbc = Rb Rcf / (Rb + Rcf) = ( 220 k x 470 k ) / ( 220 k + 470 k ) = 150 k ohms.

Now we calculate the gain.

Av = mu Rbc / ( rp + Rbc ) = 100 x 150 k / ( 80 k + 150 k ) = 65.2

### Example 4.2

A triode tube is to be used as a single ended low power amplifier. The output transformer has a primary impedance of 3000 ohms. Think of Rb being 3 k ohms and Rcf as not present. Which of the following tubes will give the greatest voltage gain?

12AT7, Amplification Factor = 60, Plate Resistance = 10900
12AU7, Amplification Factor = 17, Plate Resistance = 7700
12AV7, Amplification Factor = 41, Plate Resistance = 4800
12AX7, Amplification Factor = 100, Plate Resistance = 80000

### Solution.

The gain for each is given by,

Av = mu Rb / ( rp + Rb )

For the 12AT7 it is,

Av = 60 x 3000 / ( 10900 + 3000 ) = 12.9

For the 12AU7 Av = 4.77
For the 12AV7 Av = 15.8
for the 12AX7 Av = 3.61

The 12AV7 comes in first with 15.8 and the 12AT7 is runner-up at 12.9. Notice that the 12AX7 with its impressive amplification factor of 100 comes in last at 3.61. A high amplification factor may not guarantee a high gain amplifier.

### Example 4.3

A 12AX7 which is without a cathode bypass capacitor has a plate load resistor, Rb, of 220 k ohms, a cathode resistor, Rk, of 3300 ohms, and the grid resistor of the following stage, Rcf, is 470 k ohms. Tube manual data on the 12AX7 gives Amplification factor = 100 and plate resistance = 80 k ohms. What is the gain of this 12AX7 amplifier

### Solution

Without a cathode bypass capacitor the gain is given by,

Av = mu Rbc / (rp + Rbc + Rk (mu + 1))

Remembering from Example 4.1 the parallel combination of Rb and Rcf = 150 k ohms and substituting all values gives,

Av = 100 150 k / (80 k + 150 k + 3300 x 101 ) = 26.6

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