# Amplifier design with three stages

As a project for my electronics 101 class, I've been assigned to design a three stage amplifier using bjt transistor to achieve a gain of 150 and input resistance of 100k and output resistance of 50 ohms .I have tried to do so, but the result is less than satisfactory, I really need the help of an expert.(The question might sound basic to you,so sorry that I'm a beginner.)

I know for a fact that this circuit has many flaws. First of all the output resistance is not 50,It's 90. Secondly,The 200k resistance that I've used at the beginning of the circuit to make the high input resistance,dampens the signal,so in a sense, my circuit dampens the signal at first and then amplifies it. Thirdly, my dc sources are too many, I can make use of only one dc source,so this last problem is not really something that I worry about.And my gain is something about 105 which is not satisfactory.

1.I would really appreciate it if you help me on this.I think I should use a Common Collector stage as the last stage,but I have trouble configuring/understanding the output resistance of a common collector stage.

1. I have no idea how I should make the input resistance as high as 100k without dampening my signal.

3.Do you think the correct configuration to achieve gain of 150 is CE-CE-CC?

As I've said before,I would really appreciate your help.I'm pretty much clueless on how to even begin improving my design to match the specifics of the assignment.So any help, big or small is needed.

• Hmm can you use a supply voltage larger than 12V? Can you describe how you choose R3 and R4? If you get rid of R1 then what determines your input impedance? And yes I think a CC output stage may help meet your 50 ohm output impedance spec. – George Herold Nov 25 '14 at 13:20
• Are you required to use npn transistors only? Or is a pnp stage allowed (because of dc operating points). Don`t use a series input resitor (200k). Instead, try a common emitter stage with feedback (cancel C2). – LvW Nov 25 '14 at 14:18
• What frequency band does the amplifier need to work over? – The Photon Nov 25 '14 at 17:23
• Something is seriously messed up with your schematic. It shows the outputs shorted, both connected to ground. The input signal at the top of C1 is also shorted to ground. – Olin Lathrop Feb 24 '15 at 15:31
• I suggest to use a common collector stage (emitter follower) at the 1st stage because it has high input impedance and low output impedance (= what you want) – Curd Feb 24 '15 at 16:53

Your electronics class has probably taught you the hybrid-pi model and given you some complex (yet accurate) formulas for gain, input resistance, and output resistance of the various amplifier topologies. It might help your understanding to have some simpler, approximate formulas. These come from the always-helpful Art of Electronics by Horowitz and Hill.

simulate this circuit – Schematic created using CircuitLab

$$Current\ gain = \frac{I_C}{I_B} = h_{FE} = \beta$$

$$Input\ resistance\ of\ the\ base: \beta R_E$$

$$Output\ resistance\ of\ the\ emitter: \frac{R_S}{\beta} || R_E$$

$$Output\ resistance\ of\ the\ collector: R_C$$

$$Voltage\ gain = \frac{V_C}{V_{in}} = -\frac{R_C}{R_E}$$

These formulas are based on the following assumptions, some of which may be interchangeable:

• $\beta$ is large

• $R_E >> r_e$

• The voltage drop across the base-emitter junction is constant

• The collector current is not too large

As $R_E$ gets smaller, the inherent emitter resistance starts to have a bigger effect on your gain. As the collector current gets larger, the transistor starts acting less like an ideal current source. This is where the $r_\pi$ and $r_o$ terms from the hybrid-pi model come in. In particular, the common case of a bypassed emitter resistor (which gives you the high gain you need) requires the hybrid-pi model.

As you can see, using series resistors to directly control the input resistance is not necessary. The emitter resistor's value gets multiplied at the base. Just make sure your biasing resistors are large, and you should be fine. As you suspected, a common collector amplifier will give you the output resistance you need.

I'd probably consider CE,CE, CC as the best approach to lead to the performance you want with stage 1 and stage 2 providing gain that overall gives 150. Another possible problem that I see is the bias points for each CE stage you have. For instance, the dc voltage across the emitter resistors is normally (rule of thumb) made to be 10% of Vcc but it looks like you are biasing the base with 6 volts via a 20k - this is likely to lead to an emitter voltage of about 4 or 5 volts.

Given Vcc is 12 volts this seems too high so lower the 6 volt bias to maybe 2 volts and this should approximately set the emitters at about 1 to 1.5 volts. Next, choose the emitter resistors to set the current through the emitter - maybe 1mA for the first stage. This means that the emitter resistor will be about 1k2.

With 1mA flowing through the collector resistor, you need to "drop" about 6V - this means a collector resistor of 6k not 2k and this should start giving you more gain in the front end transistor stage.

Step and repeat with probably 3mA or 4mA emitter current for the 2nd stage.

This is not my area of expertise. But I think you should be copying the basic op-amp topology. The first stage should be a long tailed pair. The second stage can be a CE voltage amplifier, and the third stage can be a current buffer (emitter follower). Focus on high gain and biasing for wide Voltage swing. You can set the precise gain with feedback later. Take this for what it is worth. I would have trouble completing this assignment myself, but I am sure I would start with a long-tailed pair, followed by a common emitter (darlinton, maybe?) and from there I would see how it was going. Ten million op-amps can't be wrong.