1. Modifications to the Basic Transistor Model
So far, we’ve assumed a simple model for transistors:
VBE = constant = 0.6 V
IE ≈ IC = IB
But this simple picture breaks down when we try to get greedy:
The basic model predicts G   as RE  0, but this is not the case
“Electronic Justice” prevails!
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)

2. Ebers-Moll Equation
Gain is limited because VBE varies with IC according to the Ebers-Moll equation:
IS = saturation current (depends exponentially on temperature)
VT = kT / q = 25.3 mV at room temp.
k = Boltzmann’s constant, T = temperature in Kelvin, q = charge of the electron
Since IC >> IS (on)
 IC ≈ IS exp(VBE / VT)
VBE increases by ≈ 60 mV for every decade increase in IC or by ≈ 18 mV for every doubling of IC
(Lab 5–1, 5–4)
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

3. Implications of Ebers-Moll Equation
There is an intrinsic resistance associated with the emitter (re)
Pretend it is a resistor in series with the emitter
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

4. Implications of Ebers-Moll Equation
Temperature effects
VBE decreases by ≈ 2.1 mV per °C, holding IC constant
IC increases at about 9% per °C, holding VBE constant
From massaging the equation a little
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

5. Complication: Early Effect
IC grows as the voltage across the transistor (VCE) grows, caused by changing effective base width
If IC is assumed fixed, this effect looks like an effect on VBE:
≈ )
Another interpretation of the Early Effect is that there is a variation in IC while VBE is fixed
Thus transistors are not perfect current sources!
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

6. Emitter-Follower Revisited
re prevents the output impedance from getting too small
Vout
Vin RE RL
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

7. Common-Emitter Amplifier Revisited
re caps the gain of the grounded-emitter amplifier
Assume IC (quiescent) = 1 mA. Then re = 25  and G ≈ –200, but G is not constant since re is not constant (IC not constant)
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

8. Common-Emitter Amplifier Revisited
This change in gain (from the changing re) results in a “barn-roof” distortion of the output waveform:
(Lab 5–2)
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

9. Common-Emitter Amplifier Revisited
Fix: add an emitter resistor much larger than re
RE reduces output signal error at the cost of gain
Electronic justice prevails again!
Typically don’t use a grounded common-emitter amplifier
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

10. Negative Feedback RE also provides beneficial “negative feedback”:
IC begins to grow with increased temperature
VE rises, as a result of increased IC (Ohm’s law)
Rise in VE lowers VBE since VB is fixed, and so IC is reduced according to Ebers-Moll equation (like closing the transistor “valve”)  better temperature stability
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

11. Common-Emitter Amplifier Revisited
For temperature stability and high gain, bypass RE with a capacitor (remember Lab 3–6):
RE “disappears” at high frequency as ZC  0
But this circuit still distorts the output signal
(Lab 5–2)
Helps temp. instability problem 
 Helps improve gain
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

12. More Negative Feedback
Another example of (DC) negative feedback:
The negative feedback makes the quiescent DC level of the collector more stable
However the feedback is quite small (< 0.1%) at signal frequencies, so signal gain is essentially undisturbed
(Lab 5–5)
= RC
VC (quiescent) ≈ 7 V
R1 = VC
0.6 V
0 V
R2 =
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

13. Matched Biasing Transistor
Matched transistor pairs are used to stabilize base voltage for the required collector current
Ensures automatic temperature compensation
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

14. Current Mirrors
The concept of matched base-emitter biasing is useful in making current mirrors
(Lab 5–3)
VE = 15 V
VB = 14.4 V
VC = 14.4 V
≈ Iprogram
Iprogram
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

15. Temperature Effects on Current Mirrors
However Iout does not match Iprogram very well when the temperatures of the two transistors become unequal
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

16. Temperature Effects on Current Mirrors
You can beat the effects of temperature variations by using matched transistors on a monolithic IC array (i.e. made on the same chunk of silicon)
Both transistors stay at the same temperature
(Lab 5–3)
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

17. Early Effect on Current Mirrors
Another problem: Iout and Iprogram will differ to the extent that VCE differs across each transistor (consequence of Early Effect)
VE = 15 V
VB = 14.4 V
VC = 14.4 V
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

18. Defeating Early Effect in Current Mirrors
Fix: add an emitter resistor that provides negative feedback to fight the growth of Q2’s IC
The cost is a somewhat decreased compliance range of Q2
+15 V Q1 Q2 VE VB VC
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

19. Defeating Early Effect in Current Mirrors
A better fix: use the Wilson Mirror circuit
Clamps VCE for both Q1 and Q2 so a relative change in VCE does not occur between them
(Lab 5–3)
+15 V
14.4 V
14.4 V
13.8 V
(Student Manual for The Art of Electronics, Hayes and Horowitz, 2nd Ed.)

20. Push-Pull Emitter Follower
Suppose you wanted to drive a low-impedance (8 ) speaker using an emitter-follower transistor:
A rather large base current of at least 50 mA is needed for Q2 in order to meet the power requirements of the speaker (9 Vrms across 8 )
More power is consumed in the circuit than is delivered to the speaker
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)

21. Push-Pull Emitter Follower
A push-pull follower does the same job but with much smaller power dissipation
Average power dissipated in each transistor is about 2 W, considerably less than the 10 W delivered to the load
Speaker behaves like a load resistor to ground:
Rspeaker
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)

22. Push-Pull Emitter Follower
An undesirable consequence of this circuit is “crossover distortion” when –0.6 V  Vin  +0.6 V
See text for a solution to this problem
(Lab 5–6)
Q1 conducting
Q2 conducting
(The Art of Electronics, Horowitz and Hill, 2nd Ed.)