General Parameters of Amplifiers

BJT amplifiers are built in one of three configurations — CB, CC or CE — chosen for a particular application on the basis of their characteristic parameters. To select the right amplifier we must know these general parameters. Consider the general representation of an amplifier (Figure 3.2.1) with AC input voltage v_i and current i_i, and AC output voltage v_o and current i_o. Amplifiers are described by five characteristic parameters together with their bandwidth.

Gain and impedance parameters

1. Current gain (A_i) — the ratio of output current to input current: $A_i = i_o / i_i$.
2. Voltage gain (A_v) — the ratio of output voltage to input voltage: $A_v = v_o / v_i$.
3. Power gain (A_p) — the ratio of output power to input power: $A_p = p_o / p_i$. Power gain also equals the product of voltage gain and current gain: $A_p = A_v \times A_i$.
4. Input impedance (Z_i) — the ratio of input voltage to input current: $Z_i = v_i / i_i$.
5. Output impedance (Z_o) — the ratio of output voltage to output current: $Z_o = v_o / i_o$.

Bandwidth

The frequency response of an amplifier (Figure 3.2.2) is a plot of its voltage gain against frequency. The difference between the higher and lower cut-off frequencies is called the bandwidth: $BW = f_H - f_L$. At the cut-off frequencies f_H and f_L the voltage gain equals (or exceeds) 70.7% of its maximum value; these are also called the half-power frequencies, because the power delivered at them is half of its maximum.

Half-power frequency (3 dB frequency)

The lower and upper cut-off frequencies f_L and f_H are also called 3 dB or half-power frequencies. When the voltage falls to $1/\sqrt{2}$ (0.707) of its maximum value, the power — which is proportional to the square of the voltage — falls to $(1/\sqrt{2})^2 = 1/2$ of its maximum. The name '3 dB' comes from the fact that the voltage gain at these frequencies is 3 dB below the maximum. For distortionless amplification the signal's frequency range must lie within the amplifier's bandwidth.

Decibel gain

The gain of an amplifier is simply a number, but for practical importance it is given the unit bel or decibel. The power gain in bel is the common (base-10) logarithm of the power gain:

where P_i and P_o are the input and output powers. The bel is a large unit, so the decibel (dB) — one-tenth of a bel — is used in practice. Since power is proportional to the square of the voltage,

$\text{Gain (dB)} = 10\,\log_{10}(P_o / P_i) = 10\,\log_{10}(v_o / v_i)^2$ …