Multistage Amplifiers

Review

1. Solve DC Bias (Can be Hard)
2. Identify Stages (Hard)
3. Split Circuits along stages (Easy)
4. Reduce each stage to equivalent amplifier (Easy)
5. Connect stages together to analyze over all response (Easy)

Complex Example

1. Figure 6.46 circuit
2. Identification of pieces
   1. Q9 diode connected voltage bias
   2. Q3, Q6 current supplies for mirrors
   3. Q1 and Q2 form diff pair input stage
   4. Q4 and Q5 forms diff pair gain stage
   5. Q7 level shifer
   6. Q8 output stage emitter follower
3. DC Bias
   1. I(Q9) = 15-0.7V/28.6k = 0.5mA
   2. I(Q3) = 0.5mA (mirrors Q9)
   3. I(Q1) = I(Q2) = 0.25mA
   4. I(Q6) = 4 * I(Q9) = 2mA
   5. I(Q4) = I(Q5) = 1mA
   6. I(Q7) = (3-0.7) / 2.3k = 1mA
   7. I(Q8) = (15.7-0.7) / 3k = 5mA
4. Stage by stage analysis
5. Stage 1 - Input Fully Differential Pair
   1. R_id = 2 r_pi = 2 (ß+1) V_t / I_C = 2 * 101 * 25mV / 0.25mA = 20k
   2. R_out = 2 R_C = 40k
   3. A_vo = g_m R_out / 2 = I_C / V_t * 40k / 2 = 0.25mA / 25mV * 20k = 200V/V
6. Stage 2 - Single Ended Differential Pair
   1. R_id = 2 r_pi = 2 (ß+1) V_t / I_C = 2 * 101 * 25mV / 1mA = 5k
   2. R_out = R_C = 3k
   3. A_vo = g_m R_out / 2 = I_C / V_t * 3k / 2 = 1mA / 25mV * 3k / 2 = 60V/V
7. Stage 3 - PNP Common Source with 2.3k resistor in the source
   1. R_in = r_pi + (ß+1) R_E = (ß+1) V_t / I_C + (ß+1) R_E = 101 * 25mV / 1mA + 101 * 2.3k = 235k
   2. R_out = R_C = 15.7.k
   3. A_vo = R_C / ( r_pi / (ß+1) + R_E) = 15.7 / (2.5k/101 + 2.3k) = 6.75
8. Stage 4 output stage emitter follower
   1. R_in = r_pi + (ß+1) R_E = (ß+1) V_t / I_C + (ß+1) R_E = 101 * 25mV / 5mA + 101 * 3k = 304k
   2. Rout = R_E || (r_pi + R_B) / (ß+1) = 3k || (500+15.7k)/101 = 152ohms
   3. A_vo = 1
9. Overall Amp
   1. R_id = Stage 1 = 20k
   2. R_out = Stage 4 = 152ohms
   3. Avo = 200 * (5k / 45k) * 60 * (235k / 238k) * 6.75 * (304k / 320k) * 1 = 8442V/V

Conclusions

• Multistage Amps Complex Example

Next Time

• MOS Capacitances