Download Modifications to the Basic Transistor Model

Modifications to the Basic Transistor Model
• So far, we’ve assumed a simple model for transistors:
– VBE = constant = 0.6 V
– IE ≈ IC = bIB
• But this simple picture breaks down when we try to
get greedy:
vout
RC
G

vin
RE
– 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.)
Ebers-Moll Equation
• Gain is limited because VBE varies with IC according
to the Ebers-Moll equation:


– IS = saturation current (depends I  I exp  VBE   1
C
S
V 
exponentially on temperature)
  T  
– 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)
(Lab 5–1, 5–4)
(Student Manual for The Art of
Electronics, Hayes and Horowitz, 2nd Ed.)
• VBE increases by ≈ 60 mV for every decade increase in IC or by
≈ 18 mV for every doubling of IC
Implications of Ebers-Moll Equation
• There is an intrinsic resistance associated with the
emitter (re)
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
– Pretend it is a resistor in series with the emitter
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
25 
re 
I C (in mA )
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.)
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:
VBE  a VCE (a ≈ 0.0001)
– 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.)
Emitter-Follower Revisited
• re prevents the output impedance from getting too
small
Vin
(The Art of Electronics,
Horowitz and Hill, 2nd Ed.)
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
Vout
RE
RL
Common-Emitter Amplifier Revisited
• re caps the gain of the grounded-emitter amplifier
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
– Assume IC (quiescent) = 1 mA. Then re = 25  and G ≈ –200,
but G is not constant since re is not constant (IC not
constant)
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.)
Common-Emitter Amplifier Revisited
• Fix: add an emitter resistor much larger than re
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
– RE reduces output signal error at the cost of gain
– Electronic justice prevails again!
– Typically don’t use a grounded common-emitter amplifier
Negative Feedback
• RE also provides beneficial “negative feedback”:
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
– 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
Common-Emitter Amplifier Revisited
• For temperature stability and high gain, bypass RE
with a capacitor (remember Lab 3–6): (Lab 5–2)
Helps temp.
instability
problem 
 Helps
improve gain
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
– RE “disappears” at high frequency as ZC  0
– But this circuit still distorts the output signal
More Negative Feedback
• Another example of (DC) negative feedback: (Lab 5–5)
= RC
VC (quiescent) ≈ 7 V
R1 =
VC
0.6 V
0V
R2 =
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
– 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
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.)
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.)
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.)
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.)
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)
VBE  a VCE
VE = 15 V
VC = 14.4 V
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
VB = 14.4 V
Defeating Early Effect in Current Mirrors
• Fix: add an emitter resistor that provides negative
feedback to fight the growth of Q2’s IC
+15 V
Q2
Q1
VB
VE
VC
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
– The cost is a somewhat decreased compliance range of Q2
Defeating Early Effect in Current Mirrors
• A better fix: use the Wilson Mirror circuit (Lab 5–3)
– Clamps VCE for both Q1 and Q2 so a relative change in VCE
does not occur between them
+15 V
14.4 V
14.4 V
13.8 V
(Student Manual for The Art
of Electronics, Hayes and
Horowitz, 2nd Ed.)
Push-Pull Emitter Follower
• Suppose you wanted to drive a low-impedance (8 )
speaker using an emitter-follower transistor:
(The Art of Electronics,
Horowitz and Hill, 2nd Ed.)
– 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
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.)
Push-Pull Emitter Follower
• An undesirable consequence of this circuit is
“crossover distortion” when –0.6 V  Vin  +0.6 V
(Lab 5–6)
– See text for a solution to this problem
Q1 conducting
Q2 conducting
(The Art of Electronics,
Horowitz and Hill, 2nd Ed.)