# Designing a multi-stage BJT amplifier

For my final lab this semester, I've been tasked with designing a multi-stage amplifier that serves as a receiver in a laser tag set that we've been building over the course of the class. I've searched various forums, but have only found loose advice on how to go about designing the amplifier.

Here are the specifications and what I've designed so far:

Specifications:

• Gain: 5000 V/V
• Maximum output voltage: 1 V
• Built in bandpass filter with a lower corner frequency of ~200Hz and an upper corner frequency of ~20kHz
• Total current draw of less than 1 mA
• Final stage is a common collector

Here's a circuit design that should be able to fill the parameters:

simulate this circuit – Schematic created using CircuitLab

The input voltage depends on the signal received from a photodiode/resistor circuit (not depicted here). The signal will be on the magnitude of about 50 uV at the smallest.

So, as you can see, I have a 4 stage amplifier in the pattern of CE, CC, CE, CC. The way I see it, I have at least three major design steps to this project. First, I must determine the resistor values 1 through 14 such that my gain is the adequate amount. Second, I must determine the capacitor values to make the amplifier also function as a bandpass filter. Lastly, I need to limit my output to 1 V.

I'm fairly inexperienced with the design process. I know I'll need to calculate the gain, input resistance, and output resistance for each individual stage, but after that, I'm uncertain of which values to start tinkering with or adjusting to attain my goals. Before anyone jumps down my throat for wanting people to do my work for me, let me make my goal clear: I am looking for design techniques and a process that will help me solve this problem--hints in the right direction. I would be disappointed with this great community if anyone simply solved it for me. Would someone be willing to point me in the right direction?

• 1. Your capacitors are all placed so they'll give a high-pass response, just changing their values will never give you a band-pass filter. 2. Did you have a specific reason for not using active loads? 3. Did you have a specific reason for using PD+Resistor followed by a voltage amplifier instead of designing your amplifier as a transimpedance amp? Oct 25, 2016 at 4:58
• This is not my area. But the basic way to do this is in three stages. First, the input stage which is some variation on the differential pair (often with active load). The second stage is the voltage amplication stage (VAS), which will be a common emitter. You can use an active load on the collector for higher gain (if you want to achieve 5000V/V, you will need to use every trick in the book ). Maybe use a Darlington VAS. Final stage would be an emitter follower, as required. I believe it will be very challenging to get a gain of 5000 at 20kHz. Oct 25, 2016 at 5:47
• Don't worry about the bandpass. Once you get the gain you need, you can just add an input and output network to get the bandpass response. Input cap in series for lower cutoff, and output cap in shunt for upper cutoff. Oct 25, 2016 at 5:50
• The "total current draw of less than 1 mA" may further complicate the 5000 gain and the bandwidth up to 20 kHz. That frequency range read like audio, yet you say this is for laser tag? Why that particular bandwidth?
– jonk
Oct 25, 2016 at 8:09
• As you have it you are relying on only two of the BJTs for voltage gain Q1,Q3. The gain of Q1 will be approx R2/R8 and for Q3 it will be R5/R12. It will be extremely difficult (if not impossible) to get a voltage gain of 5000. Oct 25, 2016 at 9:42

Your design is a very basic and might work but since it has no feedback it is not so predictable in how it will behave in practice.

The "proper" engineer's way of designing this is by use of feedback. You basically make a crude amplifier with a high gain and enough bandwidth and use feedback to get the gain you actually want.

Unfortunately this design procedure is not something which can be explained in a few sentences. I learned this in a course which took several days and included a design assignment.

I found a University course here that should explain this method, that's 70 slides to get you started ;-)

If this is too much of a stretch in the time you have then just remember this and come back whenever a more challenging amplifier design task pops up.

Another option altogether would be to use an opamp in a feedback configuration. If you want to know more about opamp circuit design look here: Opamps for everyone

• I especially like your immediate discussion about global feedback! So true.
– jonk
Oct 25, 2016 at 7:32
• " since it has no feedback" ... The emitter resistors (R8,R12) are negative feedback effectively reducing the voltage gains of Q1,Q3 to R2/R8 and R5/R12. Adding bypass capacitors across R8 and R12 (reducing negative feedback) would increase the gain significantly but make it more dependant on individual gains of the BJT. Oct 25, 2016 at 9:50
• @JImDearden You're right, that is indeed feedback but local feedback. The feedback I'm talking about is overall feedback. In practice, an amplifier would have overall feedback to set the total gain. The stages in the amplifier could (it is not a must) have local feedback to increase bandwidth for example. Oct 25, 2016 at 10:17
• I understand that but not everyone does. Just trying to help clarify the statement. Oct 25, 2016 at 10:23
• Thank you! I appreciate the feedback. I will read up on global feedback--to be honest, this is my second class on analog circuit design and I didn't know what that was. My design was actually based on the teachers guidelines to the class and I don't have the flexibility to use an op-amp in this specific lab (the PCBs are pre-made). But thanks anyways! I will keep this advice in mind for future tasks. Oct 25, 2016 at 17:45

Design is fun because you have so many choices. Here are some rules of thumb to help you with the Q1 stage. Your have three main concerns; bias stabiltiy, gain, and frequency response. Start by biasing Q1. You get to pick your bias current. Let's choose 0.1mA because the transistor still has decent beta and it leaves you 0.9mA to play with. Next pick the collector voltage. Let's use 6v. Now we know R2=30k. For now, just assume Ic=Ie. it is close enough for what we are doing here. Next pick the emitter voltage to be 2V. Why? Because we can. This means R8 is 20k. A rule of thumb here is to choose R7 to be 10 time R8. So make it 200k. Now we do a calculation to calculate R1. Since emitter is 2V the base voltage as 2.7V. R7 current is about 13.5uA. The base current is about 0.0001/30=3.3uA. Then R1 will 9V-2.7v over the sum of these currents about 38k. So we have a basic stable stage with low gain, aprox 30k/20k or 1.5. The is because R8 is providing local feedback. This is good for DC stability but bad for gain. The solution for this is to put a capacitor across R8. Now we still have good stability because of the DC feedback but a lot of gain because we have reduced the AC feedback. Pick this capacitor to give you the low frequency corner you are looking for. You may have to split R8 into two resistors and only bypass part of the emitter resistor to get good balance of characteristics. If you have access to a simulator, you might try this. Your final bias will not be exactly 2.7 at the base or 6 at the collector but should be in the ball park. From this starting point you can make modifications and hopefully get what you need. Other stages can be designed similarly but will interact. Your emitter follower after the first stage will help prevent this but cost you current for no voltage gain. Have fun.

• Thanks! This a good place for me to start. The tip on adding a capacitor across the emitter resistor should help quite a bit. Oct 25, 2016 at 17:47