6.301 Solid State Circuits
Recitation 8: LM172 AGC AM IF Strip
Prof. Joel L. Dawson
The LM172 AGC AM IF strip gives us a rather rich set of circuit tricks to add to our toolbox. One
useful function to be able to realize in analog systems is a variable gain, where the gain is varied by
an analog signal. For example, take the following op-amp circuit:
VB
Rf
Rf
−
+
VOUT ⇒
VIN
RI
−
+
VOUT
In the small-signal view of the world, the MOSFET looks like a variable resistor (if we bias things
right). So the transfer function becomes
Rf
VOUT
=−
VIN
RI (VB )
Because RI is a function of VB .
For our class exercise, let’s explore a bipolar-friendly expression of this concept.
6.301 Solid State Circuits
Recitation 8: LM172 AGC AM IF Strip
Prof. Joel L. Dawson
CLASS EXERCISE: Consider the emitter-coupled pair:
RL
V0
VIN
RE
+
−V
− E
Remembering that gm =
(Workspace)
qI C
, derive the gain of this amplifier as a function of VE .
kT
There are other ways to implement this variable gain idea. In lecture yesterday, Prof. Roberge spoke
of “current stealing” as a way of varying the gain. We can examine that concept here in a simpler
context:
Page 2
6.301 Solid State Circuits
Recitation 8: LM172 AGC AM IF Strip
Prof. Joel L. Dawson
RL
V0
Q2
Q1
+
−
VG
Ic
QA
VIN
C BIG
Bypass to ground!
When VG = 0 , the output current from QA gets split evenly between Q1 and Q2 ….the gain is
therefore 12 gmA RL , as half of the output signal current is “stolen” by Q1 . Looking in Gray and Meyer,
we can find the function of I C that actually winds up going through RL as
IC 2
IC
β2
α2
1 + β2
=
=
⎛ V ⎞
⎛ V ⎞
1 + exp ⎜ − G ⎟ 1 + exp ⎜ − G ⎟
⎝ VT ⎠
⎝ VT ⎠
The gain for this circuit is thus
⎛
⎞
⎜
⎟
α2
⎟ gm RL
av = ⎜
⎛ VG ⎞
⎟
⎜
⎜ 1 + exp ⎜ − V ⎟
⎟
⎝ T ⎠ ⎠
⎝
Page 3
6.301 Solid State Circuits
Recitation 8: LM172 AGC AM IF Strip
Prof. Joel L. Dawson
which for
kT
( = VT ) → av ≈ gm RL
q
kT
VG << −
→ av ≈ 0
q
VG >>
The LM172 has yet another approach to solving this problem. Look at Q2 and Q3 , and see an
emitter follower (Q2 ) with a dynamic load (impedance looking into the emitter of Q3 ).
Q2
VCONTROL
Q3
⇒
VIN
VOUT
VOUT
↓
IE
↓
Now, again consulting Gray and Meyer,
IC 3 =
αF IE
⎛ V
⎞
1 + exp ⎜ − CONTROL ⎟
VT ⎠
⎝
, IC 2 =
αF IE
⎛V
⎞
1 + exp ⎜ CONTROL ⎟
⎝ VT ⎠
For an emitter follower with resistance RE in the emitter, the voltage gain is
av =
( β + 1) RE
rπ 2 + ( β + 1) RE
Page 4
(Q3 )
6.301 Solid State Circuits
Recitation 8: LM172 AGC AM IF Strip
Prof. Joel L. Dawson
But here, RE =
rπ 3
. Assuming all β s are equal,
β +1
av =
rπ 3
rπ 2 + rπ 3
Recalling that rπ is inversely proportional to I C
rπ = β
VT
IC
We can qualitatively sketch rπ 2 and rπ 3 as a function of VCONTROL :
rπ 2 , rπ 3
rπ 3
rπ 2
VCONTROL
βVT
IE
The corresponding gain graph for this circuit would then look something like
av
1
1
2
VCONTROL
There’s also an op-amp hidden in this chip. Can you find it?
Page 5
6.301 Solid State Circuits
Recitation 8: LM172 AGC AM IF Strip
Prof. Joel L. Dawson
Look at Q11 , Q12 , and Q14
+
1
gm13
R13
Q11
Q12
R14
−
R15
Page 6
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6.301 Solid-State Circuits
Fall 2010
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