-
Practical clamping circuits
If a square wave is applied as input to a clamping circuit, the
output reaches the steady-state value after a few cycles. Hence for
the input in Fig.(a) the output of the clamping circuit is given in
(b).
(a) input
(b) steady-state output Input and steady-state output of the
clamping circuit
The output at steady-state is as in figure above with voltage
levels V1, V11, V2 and V21. This output can be plotted to scale if
the voltages V1, V11, V2 and V21 are calculated. To calculate these
four unknowns, we need four equations and these four equations are
obtained as follows.fig.
(a) consider the situation at t = 0- At t = 0- , Vs =V11 and V0
= V21 The diode is reverse biased and the corresponding equivalent
circuit is
The voltage across the capacitor terminals at t=0- is
VA(0-) = Vs-Vi --------- 2
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-
Vs = V11 and V21 = Vi RRR
s +
Vi = V21 RRRs )( +
Substituting the values of Vs and Vi in equation 2
VA(0-) = V11 V21 RRRs )( +
-------- 3
(b) Consider the situation at the instant t = 0+ At t= 0+, Vs =
V1 and V0 = V1. the diode is ON and the corresponding equivalent
circuit is
The voltage across the capacitor terminals at t = 0+ is VA(0+) =
Vs Vi = V1 - Vi
V1 =Vi fs
f
RRR+
,
Vi =f
fs
RRR )( + V1
VA(0+) = V1 - f
fs
RRR )( + V1 -------- 4
Since the voltage across the capacitor cannot change
instantaneously VA(0-) = VA(0+) Hence, from equations 3 and 4
V11 - R
RR S+ V21 = V1 V1 f
fs
RRR +
-------- 5
The peak-to-peak amplitude of the input is V. Therefore V = V1
V11
From equation 5 ,V = V1 V11 = V1 f
fs
RRR +
-
RRR S+ V21 -------- 6
Once again consider the situation at t = T1- , Vs = V1 and V0 =
V11 and the diode is ON
VA(T1-) = Vs-Vi
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-
= V1 - f
sf
RRR + V11 ------- 7
Similarly, at t = T1+ from the equivalent circuit, since D is
OFF
VA(T1+) = Vs Vi = V11 -
RRR S+ V2 ------- 8
Again as VA(T1-) = VA(T1 +), from equations 7 and 8
V1 - f
sf
RRR + V11 = V11 - R
RR S+ V2
V = V1 V11 = f
sf
RRR + V11 - R
RR S+ V2 ------- 9
Further at t = 0+, V0 = V1 and in the interval 0 to T1, V0
decays with a time constant (Rf+Rs)C
Hence, V11 = V1CRR
T
sfe)(
1
+
--------- 10 Similarly in the interval T1 to T2, the diode is
reverse biased and the circuit time constant is (Rs+R)C The voltage
V2 decays to V21
V21 = V2 CRR
TT
se)()( 12
+
--------- 11 Equations 6, 9, 10 and 11 will enable us to
determine the voltage V1, V11, V2 and V21. If in the above circuit
Rs = 0. Equations 6 and 9 reduce to V = V1-V21 = V11 V2 -------- 12
It is evident from the above discussion that the output is
independent of the levels V1 and V11 associated with the input and
is only determined by the amplitude V. Subtracting equation 9 from
equation 6
f
sf
RRR + (V1 V11) - R
RR S+ (V21-V2) = 0 ------- 13 If V1-V11 = f and V21 V2 = r From
Equation 13
f
sf
RRR + f = R
RR S+ r
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f = fs
f
RRR+
.
RRR S+
r
If Rs
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