Using 2N3904 for 3V audio preamp

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I want to use a 3.3 volt supply to power a voltage divider biased pre-amplifier using a 2N3904. My input signal level is 50mv p-p with a 50 ohm source resistance. I am looking for a gain of about 50. After doing the math and building the circuit, my design works, but in order to get a adequate quiescent point I have to use small valued resistors. As a result of this, I end up with a very low complex input impedance when I connect my signal source.
My question is what would be a better approach to the amplifier design?
 
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Try something like this:
FIG_TS-6-19.gif

The gain is approximately 1 + R4/R5.
 
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Thanks everyone for your help. I am sure if I replied properly to Svein, but it looks like there is the usual voltage divider bias circuit consisting of Q1 with the addition of Q2. It looks like Q2 is being used as time varying current valve. When the collector voltage at Q1 is lower than the voltage at the base of Q2 (Vcc-vbe of Q2) then Q2 conduct a current which generates a time varying voltage across R4 and R5. Q2 also functions to not load or disturb the Q point of Q1. That AC signal can be coupled through C2. Now my load will see a AC output impedance of Xc2 (capacitive reactance of C2) plus R4 + R5 or just R4 + R5 if I neglect C2's impedance effects. Is my interpretation correct? Thanks
 
Inventive said:
Is my interpretation correct?
Yes - sort of.

Now - back your original problem. I am not sure that the circuit I copied for you is the complete answer to your needs. The 2N3904 has a minimum beta or current gain of 100. Getting a gain of 50 out of a single transistor circuit is going to be problematic. I shall sketch some additional solutions for you to choose between (my motto is: Do not commit yourself until you have at least 5 solutions to choose between).
  1. Use a low voltage operational amplifier like OPA322 (http://www.ti.com/product/opa322/datasheet) and connect it in a positive gain configuration.
    upload_2017-3-9_16-9-42.png
    The gain is 1 + Rf/Rg
  2. Use a CMOS inverter (4069UB) and connect it as an amplifier
    cmos-amp-png.73527.png
  3. Use a self - biasing amplifier, like this:
    upload_2017-3-9_16-9-42.png
  4. Use a JFET instead of the 2N3904. This will give you a higher input impedance
    amp14.gif
  5. Or go with the circuit I gave you, but modify it until it works (I would personally try to self-bias the first stage as in point 3. above
(Edit) Somehow the circuit that should be attached to point 1 is shown as an attachment in the bottom of my post and the circuit belonging to point 3 is shown instead - I don't know why!
 

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Svein said:
Yes - sort of.

Now - back your original problem. I am not sure that the circuit I copied for you is the complete answer to your needs. The 2N3904 has a minimum beta or current gain of 100. Getting a gain of 50 out of a single transistor circuit is going to be problematic. I shall sketch some additional solutions for you to choose between (my motto is: Do not commit yourself until you have at least 5 solutions to choose between).
  1. Use a low voltage operational amplifier like OPA322 (http://www.ti.com/product/opa322/datasheet) and connect it in a positive gain configuration.
    View attachment 114291 The gain is 1 + Rf/Rg
  2. Use a CMOS inverter (4069UB) and connect it as an amplifier
    cmos-amp-png.73527.png
  3. Use a self - biasing amplifier, like this:
    View attachment 114291
  4. Use a JFET instead of the 2N3904. This will give you a higher input impedance
    amp14.gif
  5. Or go with the circuit I gave you, but modify it until it works (I would personally try to self-bias the first stage as in point 3. above
(Edit) Somehow the circuit that should be attached to point 1 is shown as an attachment in the bottom of my post and the circuit belonging to point 3 is shown instead - I don't know why!
Thanks for you help. I found a CD4069 hex inverter in my supply of parts, and a n channel JFET. I think I will take your advice and try many different configurations that have shown me. I majored in electronics (B.S.) a long time ago and have become interested in circuit design and it's application again as a hobby. With my first circuit I though a gain 50 could be attained with a single transistor using the r'e model since I am working at lower frequencies. Thanks again for your time.
 
Thanks everyone for your input. I went with the FET approach