Power rating is an important consideration in selecting bias resistors since they must be capable of withstanding the maximum anticipated (worst case) power without overheating. Power considerations also affect transistor selection. Designers normally select components having the lowest power handling capability suitable for the design. Frequently, de-rating (i.e., providing a "safety margin" from derived values) is used to improve the reliability of a device. This is similar to using safety factors in the design of mechanical systems where the system is designed to withstand values that exceed the maximum.
Consider a common emitter amplifier circuit shown in fig. 1.
Fig. 1
Derivation of Power Equations
Average power is calculated as follows:
For dc:
(E-1)
For ac:
(E-2)
In the ac equation, we assume periodic waveforms where T is the period. If the signal is not periodic, we must let T approach infinity in equation E-1. Looking at the CE amplifier of fig. 1, the power supplied by the power source is dissipated either in R1 and R2 or in the transistor (and its associated collector and emitter circuitry). The power in R1 and R2 (the bias circuitry) is given by
(E-3)
where IR1 and IR2 are the (downward) currents in the two resistors. Kirchhoff's current law (KCL) yields a relationship between these two currents and the base quiescent current.
IR1 = IR2 – IB (E-4)
KVL yields the base loop equation (assuming VEE = 0),
IR2 R2 + IR1 R1 = VCC (E-5)
These two equations can be solved for the currents to yield,
(E-6)
In most practical circuits, the power due to IB is negligible relative to the power dissipated in the transistor and in R1 and R2. We will therefore assume that the power supplied by the source is approximately equal to the power dissipated in the transistor and in R1 and R2. This quantity is given by
(E-7)
Where the source voltage VCC is a constant value. The source current has a dc quiescent component designated by iCEQ and the ac component is designated by ic(t). The last equality of Equation (E-7) assumes that the average value of ic(t) is zero. This is a reasonable assumption. For example, it applies if the input ac signal is a sinusoidal waveform.
The average power dissipated by the transistor itself (not including any external circuitry) is
(E-8)
For zero signal input, this becomes
P(transitor) = VCEQ ICQ
Where VCEQ and ICQ are the quiescent (dc) values of the voltage and current, respectively.
For an input signal with maximum possible swing (i.e., Q-point in middle and operating to cutoff and saturation),
Fig. 2
Putting these time functions in Equation (E-7) yields the power equation,
(E-10)
From the above derivation, we see that the transistor dissipates its maximum power (worst case) when no ac signal input is applied. This is shown in fig. 2, where we note that the frequency of the instantaneous power sinusoid is 2ω.
Depending on the amplitude of the input signal, the transistor will dissipate an average power between VCEQ ICQ and one half of this value. Therefore, the transistor is selected for zero input signal so it will handle the maximum (worst case) power dissipation of VCEQ ICQ.
We will need a measure of efficiency to determine how much of the power delivered by the source appears as signal power at the output. We define conversion efficiency as
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