1. About that tail current source

diff inclass
Figure 1. Diff pair with real tail current

  • Find the tail current symbolically.

  • Find V(outA) and V(outB).

  • What should the value of Rbias be to place V(outA) and V(outB) at the appropriate DC level? (this type of question is a good exam question)

2. Quick CM-DM coordinate system review

diff cm terms

First, review how we transform two input nodes (vA, vB) into the differential and common-mode “coordinate system” (vD, vCM).

For each of the two circuits, use KVL to compute the node voltages vA and vB.

diff cm sources
Figure 2. Simulating with CM and DM voltages



3. Common-Mode half-circuit

The common-mode half-circuit technique is useful when considering circuit behavior with pure common-mode input signals.

half circuit cm
Figure 3. Split the tail circuit
Do you see the two independent common-emitter amplifiers?

  • What is the voltage gain of each these circuits?

4. Differential-Mode half-circuit

Similarly, it is possible to draw an equivalent differential-mode half-circuit to help circuit analysis when considering pure differential-mode input signals.

half circuit diff
Figure 4. No change for AC is 0 V

If the input signal is pure differential (meaning zero AC common-mode signal), the shared emitter node voltage doesn’t change.

Example 1. Virtual ground originates from circuit analysis

See the following analysis and conclusion that derives how this emitter node becomes a “virtual ground” — which is a node whose small-signal voltage is zero but doesn’t share current with the AC equivalent circuit’s reference node ("ground"). It uses a different symbol to help make this distinction.

diff-pair-virtual-ground.pdf

Then review again this CircuitLab simulation.

Do you see the two independent common-emitter amplifiers?

  • What is the voltage gain of each these circuits?

What if the input is some combination of common-mode and differential signals?