**Decibels and Half Power Point Method:**

**Power Measurement in Decibels and Half Power Point Method –** The power gain (A_{p}) of an amplifier may be expressed in terms of the log of the ration of output power (p_{o}) to input power (p_{i}). This is illustrated in Fig. 8-4.

Thus, the decibel is the unit of power gain, or power level change.

The power dissipated in a resistance is (v^{2}/R).

Also, P_{o} = i_{o}^{2} R_{L}and P_{i} = i^{2}_{i} R_{i}

It is important to note that the above equations are correct only when the **load resistance** connected to the circuit output is equal to the **circuit input resistance**. However, it is common practice in the electronics industry to apply these equations regardless of the relationship between input and load resistances!

Amplifier output power level changes (ΔP_{0}) are also measured in decibels, and in this case the equations become,

where p_{1} is the initial output power level, and p_{2} is the new level.

where v_{1} and i_{1} are the initial output voltage and current levels, and v_{2} and i_{2} are the new levels. Equations 8-4 through 8-6 are correct so long as the amplifier load resistance remains constant.

**Half-Power Points:**

Figure 8-5 shows a typical graph of amplifier output voltage or power plotted versus frequency. Note that the frequency scale is logarithmic. The output normally remains constant over a middle range of frequencies and falls off at low and high frequencies, due to effects explained in Sections 8-3 and 8-4. The gain over this middle range is termed the mid-frequency gain. The low frequency and high frequency at which the gain falls by 3 dB are designated f_{1} and f_{2}, respectively. This range is normally considered the useful range of operating frequency for the amplifier, and the frequency difference (f_{2} – f_{1}) is termed the **amplifier bandwidth (BW)**.

Frequencies f_{1} and f_{2} are termed the half-power points, or the 3 dB points. The power output is -3 dB from its normal level when p_{2} is half p_{1}. When the amplifier output is expressed as a voltage on the graph of frequency response, the 3 dB points (f_{1} and f_{2}) occur when v_{2} is 0.707 v_{1}.