Download Lab 5: Active Decoupler Circuits

ELEC 351L
Electronics II Laboratory
Spring 2004
Lab 5: Active Decoupler Circuits
Introduction
A common problem encountered in the design of complex electronic systems is that noise (a
time-varying voltage or current made up of unwanted signals) sometimes appears on the power
supply leads. There are many possible sources of noise. For example, a noisy device, such as an
electric cooling fan, might be powered by the same voltage source; a sub-circuit may be radiating
electromagnetic energy, which induces a small voltage on the supply leads; or the leads might be
picking up radiation from an external source (such as WVBU!). Noise can sometimes find its
way into the system signal path, where it becomes superimposed on a desired signal. In the
worst cases, a positive feedback path might be created that leads to instability (oscillation). One
way to mitigate the intrusion of noise is to use an active decoupler circuit, a transistor used in
such a way that it filters out power supply noise. In this lab experiment you will investigate one
type of decoupler circuit based on a BJT.
Theoretical Background
In almost all electronic systems, multiple sub-circuits operate from a single power supply. The
sub-circuits could be amplifiers, oscillators, filters, or a wide variety of other circuits. With
respect to the power supply, a given sub-circuit can be represented as a load RL. Noise picked up
by the power supply leads can often be filtered sufficiently by connecting a decoupling capacitor
across the supply at the point where the leads enter the sub-circuit. In Figure 1a, capacitor Cb
VCC (noisy)
R1
VCC (noisy)
Cb
R1
vn
IC
IB
oib
Cb
IE
RL
+
RL
r
ib
+
VOUT
−
RL
vout
−
(a)
(b)
(c)
Figure 1. (a) Load powered by a noisy voltage source that is filtered by a simple
decoupling capacitor. (b) Active decoupler circuit. (c) Small-signal model.
1
+
−
fulfills this role. In severe cases, however, the filtering provided by Cb alone is insufficient, and
an active decoupling circuit like the one shown in Figure 1b must be used. This circuit
essentially multiplies the effectiveness of the capacitor Cb, so that the filtering it provides is
equivalent to that of a capacitor many times the size of Cb (which has a capacitive reactance
many times smaller).
To understand how the active decoupler circuit works, it is necessary to apply small-signal
analysis to the circuit in Figure 1b. The noisy power supply is modeled as a DC source of value
VCC in series with an AC source vn that represents the noise. The small-signal model is shown in
Figure 1c. The DC part of the power supply (VCC) has been deactivated, so only vn remains. The
value of Cb is assumed to be large enough so that it acts as a short circuit at the noise frequency.
The sub-circuit being powered by the noisy supply is represented by the load resistance RL. The
voltage vout represents the noise that appears across the load. The goal is to make sure that vout is
a small fraction of vn; that is, we want to minimize the ratio vout / vn.
The small-signal model in Figure 1c incorporates the simplest possible model of the BJT. Recall
that if a source (vn in this case) is isolated from a resistor network (r and RL) by a currentdependent current source (oib), and if the dependent source is a function of a voltage or current
in the resistor network (that current is ib in this case), then the current source will be inactive.
That is, in Figure 1c, oib = 0, and there is no signal current due to vn flowing through RL. Thus,
vout = 0, and the active decoupler circuit provides perfect isolation!
Of course, no decoupler circuit is perfect. To gain a better understanding of how the circuit
works, we need a slightly more accurate small-signal model of the BJT. In the analysis of BJT
circuits, we usually make the assumption that iC does not vary with vCE. However, there is, in
fact, a slight variation, and this can be seen in the i-v characteristic (plot of iC vs. vCE for various
values of iB) of a typical BJT. The curves in the active (constant-current) region are not perfectly
flat, but instead slope slightly upward. The cause of the slope is unimportant for this discussion,
but the way it is modeled is important. The collector current iC rises linearly with vCE, which
suggests that we can model the slope by placing a resistance in parallel with the currentcontrolled current source oib. We will label this resistance rce. Its value is defined by
i
1
 C
rce vCE
,
I B ,VCE
where the constraint IB, VCE indicates that the value of rce is a function of the Q-point (bias
levels) of the BJT. On most data sheets, the symbol hoe is used to represent this effect; hoe is
simply the reciprocal of rce. By incorporating rce into the small-signal model, we can obtain a
more realistic sense of the extent to which the power supply noise is attenuated by the time it
reaches the load. We will therefore use the improved small-signal model shown in Figure 2 on
the next page.
To calculate vout / vn, we first note that
vout  ib   o ib  irce RL   o ib  irce RL ,
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where we have used the approximation that o + 1 ≈ o. The currents ib and irce can be expressed
in terms of the noise and load voltages as
ib  
vout
v  vout
and irce  n
.
r
rce
Substituting these two results into the expression for vout leads to

v
v  vout 
 RL .
vout     o out  n
r
rce 

Rearranging this yields
  R
R  R
vout 1  o L  L   L vn ,
r
rce  rce

which leads to the ratio
vout RL
RL
1


.
vn
rce   o RL RL  

 o RL rce
1 
  rce 

 RL 
r
rce  
r


R1
irce
oib
vn
+
−
rce
r
ib
+
RL
vout
−
Figure 2. Improved small-signal model of the active decoupler circuit. The resistor rce
has been added to the small-signal model of Figure 1c.
In the kinds of BJT circuits we have been considering, the resistance r is usually a few thousand
Ohms. The resistance rce of typical small-signal BJTs is often 100 k or more. In light of this,
we can make the assumptions
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 o RL rce
r
 rce and
 o RL rce
r
 RL .
The expression for vout / vn can thus be approximated as
vout
r
RL

  .
 o RL rce  o rce
vn
r
Noting that
r 
VT
IB

VT  F
IC
,
where IB and IC are the quiescent base and collector currents, respectively, of the BJT, the
voltage ratio can also be expressed as
vout VT
,

vn
I C rce
where we have used the approximation that F ≈ o. Recall that  is the emission coefficient,
which typically has a value of 1 for most BJTs; and VT is the thermal voltage, which is
approximately 25 mV at room temperature. Although the noise voltage vout that appears across
RL is not zero, clearly it is greatly reduced below the value of vn. Note that the resistor R1 has no
effect on the noise-filtering behavior of the circuit; its sole purpose is to set an appropriate Qpoint for the BJT.
The active decoupler shown in Figure 1b is very effective in keeping power supply noise away
from a load; however, it has one major drawback (and a few minor ones that will not be
discussed here) which might or might not be important. The decoupler will only work if the BJT
operates in the active region; therefore, the voltage vCE must be maintained well above the
saturation level at all times. Typically, this means that the voltage across the load in the
quiescent state must be a few volts less than VCC.
The value of R1 in Figure 1b must be set so that the circuit functions properly. As mentioned
above, the resistor only affects the bias levels in the circuit. In a typical design situation, at least
two of the three quantities VL, RL, and IE (the current that flows through RL) are specified. From
this information, it is a relatively straightforward task to find the required resistor value. For
example, suppose VL and IE are specified. The quiescent base current IB flows through R1 and is
related to IE by
I
IB  E .
F
Consequently, the value of R1 can be found from
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R1 
VCC  V f  VL 
IB

V
CC
 V f  VL  F
IE
.
This requires knowledge of the value of F. However, if an average value of F obtained from a
data sheet is used instead of the exact value, the resulting error in the Q-point is often tolerable.
Experimental Procedure
Simulate a noisy power supply by adjusting the function generator to produce a 10-kHz sine
wave with a magnitude of 1 Vpp and a DC offset of 8 V. (Remember that the voltage displayed
on the function generator is not accurate if the output is connected to a load other than 50 .)
This represents a VCC of 8 V and a vn of 1 Vpp. Use a 10-k resistor to represent the load RL.
We will assume that the 50- output impedance of the function generator will not significantly
affect the results of the following experiments (except maybe the first one).

Connect a 10-F electrolytic capacitor (observe the correct polarity!) across the 10-k load
resistor to simulate the simple decoupling technique shown in Figure 1a. In this case, VCC =
VL = 8 V. Measure the “noise” voltage vout across the load, and calculate the ratio vout / vn.

Construct the active decoupler circuit shown in Figure 1b using a 2N3904 BJT and the same
10-F capacitor. Again, use the function generator to simulate a noisy power supply. Raise
the DC offset voltage from 8 V to 10 V, which simulates a VCC of 10 V. Compute an
appropriate value for R1 so that VL = 8 V with RL = 10 k. To do this, you will need the
value of F. Instead of measuring it directly, determine a reasonable estimate using the
information found in the 2N3904 data sheet, which is available at:
http://www.fairchildsemi.com/ds/2N/2N3904.pdf
Verify that the quiescent load voltage VL in your circuit is correct. If you wish, you may use
a potentiometer for R1 and adjust it to provide the proper quiescent levels.

Use the data sheet to determine a reasonable estimate for the value of rce (the reciprocal of
hoe), and then calculate the expected ratio vout / vn. Compare this result to the ratio obtained
using only a decoupling capacitor.

Apply the output of the function generator to the active decoupler circuit, and simultaneously
monitor the power supply “noise” (vn) and the noise across the load (vout) using the
oscilloscope. Calculate the measured value of the ratio vout / vn, and compare it to the
analytical value you computed in the previous step. It is possible that the noise across RL will
be so small with the decoupler in place that it will be undetectable using the oscilloscope. If
this is the case, add a resistor Rext of value 10 k or so (or lower, if necessary) across the
collector-emitter terminals of the BJT to simulate a “low” rce. This external resistance is
much smaller than rce and is in parallel with it. The effective value of rce therefore becomes
rce
effective
 rce Rext Rext .
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