Time Base Generators (part-2)

UNIT-IV: TIME-BASE GENERATORS
(Part- 2 PPT)
• Transistor constant current sweep circuit
• Current Time-Base Generators: A Simple Current
Sweep, Linearity Correction through Adjustment of
Driving Waveform, Transistor Current Time-Base
generator.
Mr. M. Balaji, Dept. of ECE, SVEC 1

Transistor constant current sweep circuit
• The sweep voltage generated by an exponential sweep generator is
non-linear as the current in the capacitor varies exponentially.
• However, to generate a linear sweep, the capacitor is required to
charge with a constant current.
• As discussed in the earlier concepts, the collector current in the CE
configuration may not remain constant with the variation in VCE.
• However, from the output characteristics of the CB configuration,
we see that for a constant value of IE, IC is independent of VCB and
the curves are parallel to the VCB axis, except for a small range of
values of VCB.

• In the output characteristics of a CB configuration, IC remains
practically constant with the variation in VCB, except, at
smaller values of VCB.
• This suggests that if a capacitor is charged using the constant
collector current of the CB configuration, the resultant
sweep voltage must be a linear sweep voltage.
• Fig. 12.7(a) shows the circuit of a transistor constant current
sweep generator using the CB configuration. From Fig.
12.7(a),
• the current IE in the base loop is:

• Let the switch S be open at t = 0.
• The collector current is constant and is given by the relation:
IC = hFBIE
Hence, C charges with the constant IC and the voltage across the capacitor
varies linearly as a function of time.
To determine the sweep voltage Vs, let us consider the small signal model of
the transistor in the CB configuration as shown in Fig. 12.7(b)

--- (1)
--- (2)
--- (3)

--- (4)
--- (5)
--- (6)
From equation (1), we get
, In equation 3, we get

--- (7)

Equation (7) reduces to

• As the second term in the bracket tends to be small, es is small.
• The constant current sweep generator shown in Fig. 12.7(a) is modified
such that a single source VYY is used to derive VEE and VCC sources, as
shown in Fig.12.8.

• In Fig. 12.8, D1 and D2 are Zener diodes.
• VEE is derived from the VYY source using these diodes such that
VEE = (VZ1 + VZ2)
where VZ1 and VZ2 are the breakdown voltages of D1 and D2.
Similarly, the VCC source is also derived using the VYY source (the
Zener current through R derives VCC).
Hence, a single voltage source is used in the circuit shown in Fig.
12.8 when compared to the circuit shown in Fig. 12.7(a). RL is the
load connected.

Principle of current time base generator
• When a constant current is made to flow through a capacitor C, voltage across capacitor would
be a voltage time base waveform
𝑉𝑐 𝑡 =
1
𝐶
න 𝑖 𝑡 𝑑𝑡
=
𝐼
𝐶
𝑡
where I/C is the slope of the voltage time base waveform.
• The dual of the above statement about current time base waveform is “ the current iL(t) flowing
through an inductor L would become a time base waveform if we maintain a constant voltage V
across an inductor.
𝐼𝐿 𝑡 =
1
𝐿
න 𝑉 𝑡 𝑑𝑡
=
𝑉
𝐿
𝑡
where V/L is the slope of the current time base waveform.

A simple current time base circuit
• The basic principle employed in current sweep generators is
electromagnetic deflection.
• In these sweep generators, when a voltage is applied to a coil of inductance
L, the current in the inductance increases linearly with time.
• A simple current sweep generator is shown in Fig. 13.1(a).
• The circuit basically consists of a transistor used as a switch driven by a
trigger signal.
• The current in the inductor rises exponentially during the period the switch
is closed (the transistor is ON).
• At the end of the trigger signal, the device switches into the OFF state and
the current in the inductor decays.

• At t< 0, Q is in cut off, so VCE= VCC; IL= 0;
• At t = 0; Q is in saturation, VCE = VCE(sat) ; so Diode D is reverse biased,
therefore iL flows through L
iL =
1
𝐿
‫׬‬ 𝑉𝐶𝐶 𝑑𝑡 =
𝑉 𝐶𝐶
𝐿
t
At t= Ts, Q is in cut off; diode D conducts, iL flows through Rd
at collector Vcc+ iL Rd develops. iL continues to flow through the diode D and
resistor Rd until it exponentially decays to zero.
The time constant of this exponential decay is τ = L/ Rd, where Rd is the sum
of damping resistance and diode forward resistance
𝑖 𝐿 𝑡 > 𝑇𝑠 = 𝑖 𝐿 𝑒
−
𝑅 𝑑
𝐿
𝑡

• When the inductor is fully charged at infinity, the current flowing through it
is only limited by the yoke resistance RL and collector saturation resistance
of transistor Rcs. Then
I=
𝑉𝑐𝑐
𝑅 𝐿+𝑅 𝑐𝑠
Generalized transient equation of an inductor is
𝑖 𝐿 𝑡 = 𝑖 𝐿 ∞ + 𝑖 𝐿(0) − 𝑖 𝐿(∞) 𝑒− 𝑅 𝐿+𝑅 𝑐𝑠 𝑡/𝐿
=
𝑉𝑐𝑐
+ 0 −
𝑉𝑐𝑐
𝑒− 𝑅 𝐿+𝑅 𝑐𝑠 𝑡/𝐿
=
𝑉𝑐𝑐
[1 - 𝑒− 𝑅 𝐿+𝑅 𝑐𝑠 𝑡/𝐿]
Expanding the exponential into series

=
𝑉𝑐𝑐
1 − (1 +
−(𝑅 𝐿+𝑅 𝑐𝑠)𝑡
𝐿
+
(𝑅 𝐿+𝑅 𝑐𝑠)2 𝑡2
2𝐿2 )
=
𝑉𝑐𝑐
(𝑅 𝐿+𝑅 𝑐𝑠)𝑡
𝐿
1 −
2𝐿
=
𝑉 𝐶𝐶 𝑡
𝐿
1 −
2𝐿
:. iL(t)=
𝑉 𝐶𝐶 𝑡
𝐿
neglect second term and iL will be iLmax when t= Ts
iL(t)=
𝑉 𝐶𝐶 𝑇 𝑠
𝐿

Slope error es
𝑒𝑠 =
ቚ
𝑑𝑖 𝐿
𝑑𝑡 𝑡
=
0
−
ቚ
𝑑𝑖 𝐿
𝑑𝑡 𝑡
=
𝑇𝑠
ቚ
𝑑𝑖 𝐿
𝑑𝑡 𝑡
=
0
iL =
𝑉𝑐𝑐 𝑡
[1 - 𝑒− 𝑅 𝐿+𝑅 𝑐𝑠 𝑡/𝐿
]
𝑑𝑖 𝐿
𝑑𝑡
=
𝑉 𝐶𝐶
𝐿
(1- 𝑒− 𝑅 𝐿+𝑅 𝑐𝑠 𝑡/𝐿
)
ቚ
𝑑𝑖 𝐿
𝑑𝑡 𝑡 = 0 =
𝑉 𝐶𝐶
𝐿

ቚ
𝑑𝑖 𝐿
𝑑𝑡 𝑡 = 0 =
𝑉 𝐶𝐶
𝐿
(1- 𝑒− 𝑅 𝐿+𝑅 𝑐𝑠 𝑇𝑠/𝐿
)
𝑒𝑠 =
ቚ
𝑑𝑖 𝐿
𝑑𝑡 𝑡
=
0
−
ቚ
𝑑𝑖 𝐿
𝑑𝑡 𝑡
=
𝑇𝑠
ቚ
𝑑𝑖 𝐿
𝑑𝑡 𝑡
=
0
es =
𝑅 𝐿+𝑅 𝑐𝑠 𝑇𝑠
𝐿

we know iL =
𝑉 𝐶𝐶 𝑇 𝑆
𝐿
𝑇𝑠
𝐿
=
𝑖 𝐿
𝑉 𝐶𝐶
:. es =
(𝑅 𝐿+𝑅 𝑐𝑠)𝑖 𝐿
𝑉 𝐶𝐶
to maintain linearity, iL (𝑅 𝐿 + 𝑅 𝑐𝑠) ≪ 𝑉𝐶𝐶

Linearity Correction through Adjustment of Driving Waveform
The non-linearity encountered in the previous circuit is:
as the inductor (yoke) current increases, the current in the internal resistance
of the source Rs also increases. Consequently the voltage across the inductor
decreases (as shown in Figure below).

So, vL = Vs − iLRs as vs is constant at Vs.
If we can compensate for the voltage developed across the resistance Rs then
the current sweep tends to be linear.
This can be achieved as shown in figure below.
-

Let Rs be the internal resistance of the source vs.
The total circuit resistance is (Rs + RL ).
Now, if we want the inductor current to vary linearly, i.e., iL = Kt
(where K is the constant of proportionality) then the source voltage vs is,
This waveform consists of a step followed by a ramp (Rs+RL)Kt. Such
a waveform is called a trapezoidal waveform.

We can thus see that if the driving signal is trapezoidal as given by Equation
above, then the current sweep is linear (i.e., iL = Kt).
The Norton representation of the driving source, using Eq.(13.3) is:
The waveform of this current source is also a step followed by a ramp (as
shown in Figure in next slide). Thus, a trapezoidal driving waveform
generates a linear current sweep.
At the end of the sweep, the current once again will return to zero
exponentially with a time constant τ = L/(Rs + RL).
Generally, Rs >> RL, hence, τ ≈ L/Rs.

The question now is, should Rs be small or should it be large?
The resistance Rs is chosen based on two conflicting requirements.
If Rs is small, the current will decay slowly and a long period will
have to elapse before another sweep is possible, i.e., the fly-back
time becomes unacceptably long. This could be construed as a
disadvantage.
However, the advantage is that the peak voltage developed across
the inductor (= ILRs) may not be unduly large.
As a result, the voltage at the collector of the transistor when the
sweep terminates (= VCC + ILRs), which reverse-biases the base-
collector diode of the transistor may not be large enough to
damage the device.

Alternately, if Rs is large, the current will decay rapidly.
This means that the retrace time is negligible, which
enables us to initiate the next sweep immediately after the
sweep duration.
For this, Rs is required to be large. However, a large peak
voltage will appear across the inductor and the voltage that
now reverse-biases the base-emitter diode of the transistor
may be excessively large and can damage the device.

Generally, a compromise has to be struck such that the spike
amplitude is not appreciably large and also the inductor current
decays in a smaller time interval.
Normally, to achieve this, a damping resistance Rd is connected
across the yoke to limit the peak voltage.
Let R be the parallel combination of Rs and Rd .
Then the retrace time constant is τr = L/R.
The trapezoidal waveform required to improve the linearity of the
current sweep is generated using the circuit shown in next slide,
we have:

Vo = V – I R2

Expanding the exponential as a series and limiting to the first few terms
of the expansion, we have:

Thus, the first term is a step and the second term represents a ramp.
Therefore, vo is a step followed by ramp (trapezoidal).

Transistor Current Time-Base generator

Here, Q1 acts as switch which serves the function of S, it is ON when the
input is zero and is OFF when the input goes negative.
R1, R2 and C1 generate the trapezoidal driving waveform.
Q2 and Q3 combination is a Darlington pair and RE stabilizes iL.
The Darlington emitter follower provides a large input resistance and thus
eliminates the loading on the driving source by its input.
The current iL varies linearly with time.

When the transistor is in saturation, the entire voltage Vcc will appear
across the inductor. If the current reaches the maximum value IL max in
time Ts, then

Time Base Generators (part-2)

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