Hello, I am currently reading the section about bootstrapping (page 112) of the book "The Art Of Electronics (3rd edition)". The core concept of bootstrapping is explained nicely, however I'm struggling to understand how to choose the resistors \(R_1\), \(R_2\) and \(R_3\) in the attached circuit.
On page 84 there is a design receipt printed for the standard emitter follower:
Step 1. Choose \(V_E\).
For the largest possible symmetrical swing without clipping, \(V_E=0.5 \cdot V_{CC}\), or +7.5
volts.
Step 2. Choose \(R_E\)
For a quiescent current of 1mA, \(R_E=7.5k\)
Step 3. Choose \(R_1\)and \(R_2\).
\(V_B\) is \(V_E+0.6V\), or \(8.1V\). This determines the ratio of \(R_1\) to \(R_2\) as 1:1.17. The preceding loading criterion requires that the parallel resistance of \(R_1\) and \(R_2\) be about 75k or less (onetenth of 7.5k×β ). Suitable standard values are \(R_2\)=130k, \(R_2\)=150k.
Everything is easy until step 3. But how to choose now (with the bootstrapping concept) \(R_1\), \(R_2\)? And \(R_3\)? As far as I know, I need to know the base current of the transistor.
\[ R_3 = \frac{U_{R_3}}{I_{R_3}} = \frac{U_{R_3}}{I_{B}} = \frac{U_{R_3}}{\beta \cdot I_C} \]
But in the general case \(\beta\) is not known. How to proceed?
On page 84 there is a design receipt printed for the standard emitter follower:
Step 1. Choose \(V_E\).
For the largest possible symmetrical swing without clipping, \(V_E=0.5 \cdot V_{CC}\), or +7.5
volts.
Step 2. Choose \(R_E\)
For a quiescent current of 1mA, \(R_E=7.5k\)
Step 3. Choose \(R_1\)and \(R_2\).
\(V_B\) is \(V_E+0.6V\), or \(8.1V\). This determines the ratio of \(R_1\) to \(R_2\) as 1:1.17. The preceding loading criterion requires that the parallel resistance of \(R_1\) and \(R_2\) be about 75k or less (onetenth of 7.5k×β ). Suitable standard values are \(R_2\)=130k, \(R_2\)=150k.
Everything is easy until step 3. But how to choose now (with the bootstrapping concept) \(R_1\), \(R_2\)? And \(R_3\)? As far as I know, I need to know the base current of the transistor.
\[ R_3 = \frac{U_{R_3}}{I_{R_3}} = \frac{U_{R_3}}{I_{B}} = \frac{U_{R_3}}{\beta \cdot I_C} \]
But in the general case \(\beta\) is not known. How to proceed?
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