Professor:
What’s in a name? That which we call an amp
By any other name would behave the same;
…​
Students:
I take thee at thy word
— Fakespeare
Thevenin and Norton
diff start
Figure 1. Two-transistor amplifer

1. Revisit day19 briefly

day19: Another circuit to small-signal model

2. Differential pair

What types of amplifiers are the two stages?



Where should / can the bottom node of the BFC be connected for stabilizing the DC operating point of Q2?



What should the DC voltage at Q1-B be to make the collector currents the same?



What is the voltage at the emitter node if the base voltages are both set to 0 V?



Under the above conditions, what should the DC value of Vout be in order to maximize the signal amplitude at node out? What are the variables that influence that voltage?



3. Long-tailed pair

diff pair bjt basic
Figure 2. Basic bipolar differential pair

It is indeed possible to view this as an emitter-follower driving a common-base amplifier stage. But this hides some of the useful properties of the long-tailed or differential pair circuit.

First, we need to remove some of the assumptions we’ve been using for analyzing BJT circuits.

  • \(v_{BE} \neq 0.6\,\mathrm{V}\) (or any other constant!)

Review Tourbook Table 6. Bipolar transistor modes for the options computing voltages and currents related to a BJT.

\[i_C = I_S \exp\left(\frac{v_{BE}}{V_T}\right)\]

3.1. Gnarly math

[1] Switch to Tourbook §7.2. Bipolar differential pair.

  • Make notes here about the key ideas used in that discussion:


3.2. Sketch the plot

Plot \(i_1\) and figure out what \(i_2\) is.

\[i_1 = \dfrac{I_{tail}}{1 + \exp\left(\frac{-(v_1 - v_2)}{V_T}\right)}\]
\[v_d = \left(v_1 - v_2\right)\]


3.3. Simulate the pair

GO BACK TO the Introduction of lab4

Then, CircuitLab simulation

diff cm sources
Figure 3. Simulating with CM and DM voltages

Figure 3 is the conceptual set up of setting voltages at two nodes vA and vB by instead stating as common-mode and differential voltages.

Use KVL to find:

vA =

vB =

The lower figure shows how to use a pair of voltage-controlled voltage sources VCVS to set vA and vB. The advantage is that both sources vD and vCM are single sources, which is much more convenient for using as simululation stimuli.

Before simulating: if all input sources are 0 V, what is the DC voltage at outA and outB?

  • Plot (DC sweep): (vA, vB) vs. vCM

  • Plot (DC sweep): (vA, vB) vs. vD

Pay attention to V(E).

  • Plot (DC sweep): (outA, outB) vs. vCM.
    ¿How does this make sense?

  • Plot (DC sweep): (outA, outB) vs. vD

Input sinewaves instead and plot as voltages versus time. 3 periods with a time step smaller than 1/100th of a period.

Change the input sinewave amplitude so the output voltages clip.

1. It’s not that bad, seriously just circuit analysis.