The Transistor as an Amplifier

The Transistor as an Amplifier

– Amplification is the process of linearly increasing the amplitude of an electrical signal.

– A transistor can act as an amplifier directly using the gain, b.

– Keep in mind that when a transistor is biased in the active (linear) region, the BE junction has a low resistance due to forward bias and the BC junction has a high resistance due to reverse bias.

i) DC and AC quantities

– Amplifier circuits have both ac and dc quantities.

– Capital letters are used will be used for both ac and dc currents.

– Subscript will be capital for dc quantities.

– Subscript will be lowercase for ac quantities.

ii) Transistor amplification

– A transistor amplifies current because the collector current is equal to the base current multiplied by the current gain, b.

– Base current (I_B) is small compared to I_C and I_E.

– Thus, I_C is almost equal to I_E.

– Consider the following circuit.

– An ac voltage, V_in­, is superimposed on the dc bias voltage V_BB.

– DC bias voltage V_CC is connected to the collector through the collector resistance, R_C.

– The ac input voltage produces an ac base current, which results in a much larger ac collector current.

– The ac collector current produces an ac voltage across R_C, thus producing an amplified, but inverted, reproduction of the ac input voltage in the active region.

– The forward biased base-emitter junction present low resistance to the ac wave.

– This internal ac emitter resistance is designated r’_e.

I_e ? I_c = V_b/ r’_e

– The ac collector voltage, V_c = I_cR_C.

– Since I_e ? I_c, the ac collector voltage is V_c ? I_eR_C.

– V_b can be considered the transistor ac input voltage where V_b = V_in – I_bR_B.

– V_c can be considered the transistor ac output voltage.

– The ratio of V_c to V­_b is the ac voltage gain, A_v, of the transistor circuit.

A_v = V_c/V_b

– Substituting I_eR_C for V_c and I_e r’_e for V_b yields

A_v = V_c/V_b ? (I_eR_C)/(I_e r’_e) = R_C/ r’_e

– Thus, amplification depends on the ratio of R_C and r’_e.

– R_C is always considerably larger in value than r’_e, thus the output voltage is larger than the input voltage.

Example:

Determine the voltage gain and the ac output voltage for the following circuit if r’_e = 50 W.

Solution:

The voltage gain is

A_v ? R_C/r’_e = 1 k W /50 W = 20

Thus the output voltage is

V_out = A_vV_b = (20)(100 mV) = 2 V_rms