  24 February 2009
Author: Giorgos Lazaridis
BJT Transistor theory

Power Calculation and Efficiency

It is important to be able to calculate the power characteristics of a transistor circuit. This includes both the input and output signal power, the power gain of the circuit, the efficiency and the power dissipation on the transistor.

How to do conversions between peak-to-peak (p-p) and rms sizes

Since we are talking about AC values, there is something first that we need to make clear: There are two ways to measure a AC sizes -for example voltage-, using an rms volt-meter or using an oscilloscope. If you measure the same signal with a voltmeter and an oscilloscope, you will not get the same results. That is because the voltmeter measures the rms-voltage while the oscilloscope measures the peak-to-peak voltage. So, depending on which measuring method you use, you may need to know how to convert between rms and p-p (peak-to-peak):

urms = 0.707 x upp / 2 => urms = 0.353 x upp
upp = 2 x (1.414) x urms = 2.828 x urms

Now let's see how we can calculate the power of the input and the output signal. We will use the typical V x I formula with the rms values for voltage and current:

P = Vrms x Irms

We can apply the Ohm's law (I = V / R) on the above formula to extract a more practical one:

P = V2rms / R

The above formula is valid if the voltage is measured with a volt-meter. If you are using an oscilloscope, then you need to convert the voltage from peak-to-peak into rms. The above formula can be directly converted to use peak-to-peak values like this:

P = V2pp / 8 X R

Calculating the power gain

The formula to calculate the power gain is typical:

Ap = Pout / Pin

So we need to calculate the power on the output and on the input of the circuit. For both cases we will use one of the formulas for the power calculation from above. Usually, the last one with the peak-to-peak voltage is used. For the output power calculation, we only need to apply this formula to the load:

Pout = u2L / 8 x RL

Remember again that we are talking about the voltage on the load, and since the load is coupled through a capacitor, it can only be an AC voltage. Regarding the input power calculation, we will apply the same formula, but this time on the base of the transistor:

Pin = u2B / 8 x RB

Calculating the power gain using the hfe parameter

There is another simpler method to calculate the power gain through the voltage gain, using the hfe parameter. The voltage gain can be easily calculated for all transistor connection types as we've seen in the previous pages. Let me briefely remind the formulas for the voltage gain calculation:

Common base: Av = RC / r'e
Common Emitter: Av = uC / uB = rC / r'e
Common Colector: Av = 0.99

Since Ap = Pout / Pin, Av = Vout / Vin, Ai = Iout / Iin and P = V x I, we can re-write the Ap formula like this:

Ap = Pout / Pin = Vout x Iout / Vin x Iin => Ap = Av x Ai

But as we know, the current gain is the hfe parameter, so this leads us to the following formula:

Ap = Av x hfe

Calculating the efficiency of the amplifier

This is again a very important value, especially for battery-powered applications which require low power consumption. The efficiency is calculated by dividing the output power with the DC power that is provided:

ÃÂ· = Pout / PS x 100%

We need to calculate the DC power PS first. To do so, we only need to multiply the supply voltage VCC with the total DC current that flows through the circuit. Generally, this current is the quiescence current ICQ plus the biasing current. For all sort of biasing methods EXCEPT the voltage divider bias, the biasing current equals to the base current, and since the base current is very small compared to the ICQ, we can simply ommit it:

IS = ICQ + IB => IS Ã¢ ICQ (Not valid for Voltage Divider Bias)

But if the amplifier is biased with VDB, then we need to calculate the total current that flows through the voltage divider:

IS = ICQ + IVD => IS = ICQ + VCC / (RB1 + RB2) (Valid only for VDB)

And now we can calculate the DC power that the circuit will draw:

PS = VCC x IS

Calculating the power dissipation on the transistor

Finally, a very important value that must be calculated is the power that the transistor is called to dissipate when no AC signal is applied. This value can be calculated simply by multiplying the DC quiescence voltage and current:

PD = VCEQ x ICQ

You may now think that the power dissipation will increase if an AC signal is applied, but this is not true. If an AC signal is applied at the input, then part of the power that is being dissipated onto the transistor will be transferred onto the load (the amount depends on the efficiency of the circuit) and the power dissipation on the transistor will be decreased. Therefore, the above equation represents the maximum power dissipation. The above diagram shows how the power dissipation on the transistor PD decreases while the power on the load PL increases.

Relative pages
• Basic transistor circuits
• 555 theory of operation
• Learn how to interface ICs
• Learn how dimmers work
• The TRIAC theory
• Learn about the most popular PC Cooling methods
• Dr.Calculus: Checking transistor functionality
• Op-Amp IC Pinouts

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