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I have been having some trouble designing a long-tailed pair transistor amplifier.

Vdd2 is 5V and the 6.8k ohm resistors were already given. I am trying to get a bias voltage of 0.8V at the transistor Q3, and the maximum voltage through the emitter of the transistor should be 1mA.

The first thing I did was to select values for Rb1 and Rb2, to set the base voltage for Q1 and Q2. The base voltage I am getting is around 1V. I am getting my calculated result from the LTspice simulation as well.

The emitter voltage of Q1 and Q2 must be 0.6V less than the base voltage. However I am getting 0.946V for the emitter voltage of Q1 and Q2, 0.09V at Vbias and 0v at the emitter of Q3.

How should I change my resistor values for Rc1, Rc2 and Re in order to get Vbias around 0.8V?

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    \$\begingroup\$ You appear to be putting the cart before the horses in what you are saying. Se Vbis to give you your required current and don't worry about the voltages. \$\endgroup\$ – Andy aka Nov 3 '20 at 10:54
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A) You need to use +10 volts, so the transistors have sufficient headroom to operate in linear (non_saturated) region. Now you will have about 2 volts for the stack of transistors (constant current source, and diffpair) to operate.

B) You need to add a FOURTH transistor, down by Q3, also with 180 ohms in the emitter.

Tie the collector to base, and tie that to the base of Q3.

Then add another resistor to +Rail, that defines the current.

Try 10Kohm from that busy node (base and collector of new bipolar, plus base of Q3, PLUS the new resistor (10Kohm)) to +10 volts.

C) by using biasing resistors (27K and 6.8K) of such high value, the BETA becomes important. I'd reduce those biasing resistors by 4:1, down to 8.2K and 1.8K). With that, the biasing becomes more predictable.

D) now --- what will the gain be? people suggest modeling that diffpair as (1) a emitter_follower driving a common_base

Thus wiggling Q1 base by 0.01 volts (low enough to have low distortion), will wiggle its emitter by 0.05 volts approx., and we expect to have little wiggling of Q2 base, tho you should check; if that base wiggles, then install 1uF cap.

We need the transconductance (gm) of the diffpair transistors.

With 10Kohm biasing Q4 (the new transistor) with 0.92 milliAmps, split 50% into Q1 and Q2 , the "reac" (1/gm) of each will be 26 ohms/0.46 mA == 54 ohms.

Double that , to 108 ohms.

Now divide the collector resistor 5,600 / 108 === gain of 50X.

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