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Calculating NPN Transistor Voltage Gain

May 2, 2025

Calculating Voltage Gain of NPN Transistor Amplifier

Overview

  • Discussion on how to calculate the voltage gain of an NPN transistor amplifier.
  • Formula for voltage gain:
    • ( \text{Voltage Gain} = \frac{R_{c(ac)}}{R_{e(ac)} + R_E} )
  • Terms Explained:
    • ( R_{c(ac)} ): AC collector resistance
    • ( R_{e(ac)} ): AC emitter resistance
    • ( R_E ): Emitter resistor

AC Collector Resistance

  • ( R_{c(ac)} ) is the parallel combination of ( R_C ) and the load resistor ( R_L ).
  • If no load resistor, ( R_L = \infty ), ( R_{c(ac)} = R_C ).

AC Emitter Resistance Calculation

  • Formula: ( R_{e(ac)} = \frac{25 , \text{mV}}{I_E} )
  • Steps to find ( I_E ):
    1. Calculate the base current ( I_B ).
    2. Calculate ( V_E ) (emitter voltage).
    3. Use ( I_E = (\beta + 1) \cdot I_B ).
    4. ( \beta ) (transistor's current gain)._

Base Current ( I_B )

  • Formula: [ I_B = \frac{V_{CC} - V_{BE}}{R_B + (\beta + 1) \cdot R_E} ]
  • ( V_{CC} ): Collector supply voltage
  • ( V_{BE} ): Voltage between base and emitter
  • ( R_B ): Base resistor
  • Example values:
    • ( V_{CC} = 9 , \text{V} )
    • ( V_{BE} = 0.7 , \text{V} )
    • ( R_B = 100 , k\Omega )
    • ( \beta = 100 )
    • ( R_E = 100 , \Omega )

Voltage Gain Calculation

  • After calculating ( R_{e(ac)} ), the voltage gain is: [ \text{Voltage Gain} = \frac{1000}{103.3} \approx 9.7 ]
  • Approximation: If ( R_L ) is very high, voltage gain ( \approx \frac{R_C}{R_E} )._

Example Problem: Voltage Divider Bias Circuit

  • ( \beta = 200 )
  • ( R_C = 510 , \Omega )
  • ( R_E = 220 , \Omega )
  • ( R_2 = 47 , k\Omega )
  • ( R_1 = 220 , k\Omega )
  • ( R_L = 10 , k\Omega )
  • ( C_B = 1000 , \mu F )
  • Calculate base current, emitter current, and voltage gain.

Bypass Capacitor Effects

  • Bypass capacitor decreases effective ( R_{e(ac)} ), increasing the voltage gain.
  • Potential for distortion due to lack of stabilization in gain.
  • Example of a swamped amplifier: Gain stabilized by adding non-bypassed resistor._

Swamped Amplifier

  • Stabilizes gain by adding additional non-bypassed emitter resistor.
  • Voltage gain for swamped amplifier: [ \text{Voltage Gain} = \frac{R_C}{R_{e(ac)} + R_E} ]
  • ( R_C ) is parallel combination of ( R_C ) and ( R_L )._

Conclusion

  • Understanding how component values and configurations affect voltage gain and stabilization is crucial in designing transistor amplifiers.

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