The design process for a common emitter amplifier is to set the collector voltage to be about half the supply voltage. That gives roughly equal signal swing up and down. Next decide on a collector current - lets chose 1mA and a supply voltage of 9V. So now we have 4.5V and 1mA for the collector resistor Rc = 4.5k. So lets chose the closest common E12 value of 4.7k. Next we have to choose and emitter resistor ( ie between emitter and 0V). This is where you use a rule of thumb - for an amp of that sort, about 1V across the emitter resistor is a good starting point. Since we are talking a silicon transistor with a high beta, the emitter current is very very close to the collector current. So 1V and 1mA Re= 1k for the emitter resistor.
Now we're going to bias the base using a potential divider. We need a base voltage of 1V + the base emitter voltage. This is just a diode voltage drop of about 0.65V, so we need a base voltage of 1.65V. We'll do that with a potential divider. Now this is the *only* time we need beta, and suppose that is a minimum from the spec sheet of 200. For 1mA collector or emitter current, the base current will be 5uA. So we don't have to mess around considering the base current, we'll pass twenty times the base current down the divider - so 100uA. From a 9V supply the total resistance of the divider is 9/50uA = 90k. To calculate the lower resistor Rl we use Ro = V0R/V to get 1.65x90k/9 = 16.5k, and the upper resistor Ru is 90 - 16.5k = 73.5k. So lets round to the nearest values and see where that gets us. Increase them both a bit - so upper resistor Ru = 82k and lower resistor Rl = 18k. That gives a base voltage of 18/(18+82) times 9V = 1.62V - so very close to the design target of 1.65V.
The DC voltage gain is just the ratio of the collector resistor to emitter resistor, or Rc/Re = 4.7 times. Now look what happens if the emitter current increases a bit. If it does so the voltage across the emitter resistor increases a bit. Now since the base voltage is pinned by the potential divider, the increase in emitter current reduces the base emitter voltage, which tends to decrease the emitter current. So this arrangement ensures that the bias conditions are stabilised.
Now this is still a fairly useful amplifier in its own right, with a gain of 4.7. But we want more AC gain than that. So we put a capacitor across the emitter resistor, which shorts the emitter to ground for AC signals. Now the gain equals the collector resistor divided by some other resistor due to the transistor itself. That is given by 26/emitter current (in mA). So for our 1mA design, that resistance is 26 ohms. That means that the voltage gain of our amplifier is 4700/26 = 180, a very useful gain indeed.
There is actually a resonance with valve terminology here. 1/(internal emitter resistor) = gm. In this case 1/26 = 38mA/V. So the gain is gmRc = 38 x 4.7 = 180.
We need to calculate the capacitor value, for which we need to know the lowest frequency we want this amplifier to work at. Suppose that this is an audio amp and we want the low frequency limit to be 10Hz. The calculation is that at 10Hz we want the capacitive reactance to be equal to the emitter resistor. So Re = 1/(2pifCe), or C = 1/(2pifRe) . Putting in the values, Ce ~ 1/(6 x 10 x 1000) = 16uF (since 2pi is about 6). Chose the next largest standard capacitor value of 22uF.
Which completes the design. DC gain of 4.7, AC gain of 180, and an AC frequency response that goes down to 10Hz.
And I only had to use beta once!
Now we're going to bias the base using a potential divider. We need a base voltage of 1V + the base emitter voltage. This is just a diode voltage drop of about 0.65V, so we need a base voltage of 1.65V. We'll do that with a potential divider. Now this is the *only* time we need beta, and suppose that is a minimum from the spec sheet of 200. For 1mA collector or emitter current, the base current will be 5uA. So we don't have to mess around considering the base current, we'll pass twenty times the base current down the divider - so 100uA. From a 9V supply the total resistance of the divider is 9/50uA = 90k. To calculate the lower resistor Rl we use Ro = V0R/V to get 1.65x90k/9 = 16.5k, and the upper resistor Ru is 90 - 16.5k = 73.5k. So lets round to the nearest values and see where that gets us. Increase them both a bit - so upper resistor Ru = 82k and lower resistor Rl = 18k. That gives a base voltage of 18/(18+82) times 9V = 1.62V - so very close to the design target of 1.65V.
The DC voltage gain is just the ratio of the collector resistor to emitter resistor, or Rc/Re = 4.7 times. Now look what happens if the emitter current increases a bit. If it does so the voltage across the emitter resistor increases a bit. Now since the base voltage is pinned by the potential divider, the increase in emitter current reduces the base emitter voltage, which tends to decrease the emitter current. So this arrangement ensures that the bias conditions are stabilised.
Now this is still a fairly useful amplifier in its own right, with a gain of 4.7. But we want more AC gain than that. So we put a capacitor across the emitter resistor, which shorts the emitter to ground for AC signals. Now the gain equals the collector resistor divided by some other resistor due to the transistor itself. That is given by 26/emitter current (in mA). So for our 1mA design, that resistance is 26 ohms. That means that the voltage gain of our amplifier is 4700/26 = 180, a very useful gain indeed.
There is actually a resonance with valve terminology here. 1/(internal emitter resistor) = gm. In this case 1/26 = 38mA/V. So the gain is gmRc = 38 x 4.7 = 180.
We need to calculate the capacitor value, for which we need to know the lowest frequency we want this amplifier to work at. Suppose that this is an audio amp and we want the low frequency limit to be 10Hz. The calculation is that at 10Hz we want the capacitive reactance to be equal to the emitter resistor. So Re = 1/(2pifCe), or C = 1/(2pifRe) . Putting in the values, Ce ~ 1/(6 x 10 x 1000) = 16uF (since 2pi is about 6). Chose the next largest standard capacitor value of 22uF.
Which completes the design. DC gain of 4.7, AC gain of 180, and an AC frequency response that goes down to 10Hz.
And I only had to use beta once!
