Differential Amplifier - Active Load Current MIrror Logic
Fundamentally, in the small_Signal model, in a transistor_driving_R_load stage, the gain will be

gm * ( Rload || R_early_effect)

whereas in transistor_driving_activeLoad stage, the gain will be

gm * (R_early_effect || R_early_effect)

With R_early_effect able to be &gt;&gt; R_load , the gain with the active_load can be &gt;&gt; gain of the transistor_driving_R_load.
(R_load is a physical resistor, whereas R_early_effect is a measured parameter of the semiconductor).
Also, I recall using the 3_transistor current mirror topology (THREE Transistors), at 1 milliamp, with actual 2N2905 transistors, with emitter swamping resistors to make up for mismatched Vbe.
On a Fairchild curve tracer (perhaps one reason Schlumberger bought Fairchild Instrument), that 3_transistor current mirror measured

5,000,000 ohms

thus equivalent Early Effect voltage was ...... 5,000 volts.