Here I have taken a differential BJT pair. Both the individual gains are different and the output differential gain is also different.
Is there a problem with my circuit? Why is it happening?
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To top up on Jasen's answer and previous comments:
i) the differential amplifier is, namely, an amplifier, with a gain that is defied for differential mode and for common mode; it is usually used for diff mode, so the Vout (difference of collector voltages) is ratioed to the input voltage (the voltage applied to the two bases, from which the comment from Bimpelrekkie)
ii) the gain is given basically by gm*Rc for each arm, combined by the fact that the total current is constant as the two emitters join in common point, where the resistor R3 is connected (or, better, a current source; this for a matter of impedance ad rejection of common mode)
iii) what the amplifier does is to "reject" common mode in favor of diff mode e(that is the signal you want to process, contrasted to the external interference that is assumed common mode). So you either increase the diff mode gain, or you reduce the common mode gain, or both, resulting in a large Common Mode Rejection Ratio (CMRR) = Gain(dm)/Gain(cm)
iv) If you apply different AC signals you have a "strange" (or "unwanted") behavior, possibly where the two BJTs have different transconductance gm. Try to apply 1 signal between bases and they should share the signal 50-50.
v) The if I understand right you have VcCC=10V and VEE=10V too (but reversed in polarity). If you do not bias correctly the BJTs applying even a tiny AC signal to the BJTs results in a wide change of the operating point and they will not operate in the linear region. First:check operating points with bias voltages and currents. You should be above ground for the moment, with all bis voltages positive with respect to that. Then try the following: VCC=+20V, VEE=+10V, R3=10k, so you have 1mA total bis current. When you apply 0V as AC signal there must be 0.5mA o each side; then, as a balance, when you apply a tiny DC signal between bases, you will see a shift of DC current. If the signal is AC you do not see the result in the bias voltages and currents (thinking of calculating with Spice), but purely in the behavior as amplifier.
In order to check the proper functioning of the circuit, I recommend the following steps:
1.) Connect both input nodes to ground and verify if there is proper DC bias point
2.) Set one of the inputs to zero and check if the output signals at both collector nodes are equal in magnitude but opposite in the phase.
3.) Do the same with the other input node(s).
4.) In both cases, the gain should be app. A=(+-) 0.5 gm Rc. This gain expression results simply from the following view:
Output T1 (T2) and input at T2 (T1): The whole circuit forms a two-transistor chain - a common-collector-common-base combination.
Output T2 (T1) and input at T2 (T1): Classical common-emitter stage(s) with emitter feedback.
5.) If everything is as expected, you can perform some analyses with two inputs at the same time.