Time base Generators (part-1)

Time base Generators
Unit - IV

UNIT-IV: TIME-BASE GENERATORS
(10Periods)
• Voltage Time-Base Generators: General features of a Time Base signal,
Exponential Sweep Circuit, Constant Current Sweep Circuit, UJT Sweep Circuit,
Miller and Bootstrap Time-Base generators - basic principles, Transistor Miller
Time-Base generator, Transistor Bootstrap Time-Base generator.
• 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 2

Time base Generators:
• is an electronic circuit which generates an output voltage or current
waveform, a portion of which varies linearly with time.
Time base Generators are of two types:
• Voltage Time Base Generators − A time base generator that provides an
output voltage waveform that varies linearly with time is called as a Voltage
Time base Generator.
• Current Time Base Generator − A time base generator that provides an
output current waveform that varies linearly with time is called as a
Current Time base Generator.

General features of a Time base signal:
Sweep time Restoration time
General sweep waveform Sawtooth waveform

• After generating the sweep signals, it is time to transmit them. The
transmitted signal may be subjected to deviation from linearity when it is
transmitted through a linear network.
The deviation from linearity is expressed in three most important ways.
They are −
• The Slope or Sweep Speed Error, es
• The Displacement Error, ed
• The Transmission Error, et

The Slope or Sweep Speed Error, es
• An important requirement of a sweep is that it must increase linearly with
time, i.e. the rate of change of sweep voltage with time be constant. This
deviation from linearity is defined as

The Displacement Error, ed
• Displacement error (ed ) is the ratio of the maximum difference between the
actual sweep voltage vs, and the linear sweep, vs’ which passes through the
initial and the end points of the sweep, to the sweep amplitude.
𝑒 𝑑 =
𝑉𝑠 − 𝑉𝑠
′
𝑉𝑠
𝑉𝑠 − 𝑉𝑠
′

The Transmission Error, et
• Transmission error (et): If a ramp voltage is transmitted through a
high-pass RC circuit, the output falls away from the input
• The transmission error et is given as:
𝑒𝑡 =
𝑉𝑠
′
− 𝑉𝑠
𝑉𝑠′
Vs’ = input sweep
Vs = Output sweep

Exponential Sweep Circuit

Unijunction Transistor

UJT: Unijunction Transistor

Sweep circuit using UJT

• Design a relaxation oscillator using a UJT, with VV = 3V, η=0.68 to 0.82, Ip =
2µA, IV = 1mA, VBB = 20V, the output frequency is to be 5KHz. Calculate the
typical peak- to –peak output voltage.
• Sol:
The given UJT has the following parameters:

• Thus, R must be in the range of 17KΩ to 2.15MΩ. If R is large, C must
be very small. Therefore Choose R such that C is not very small.

• In the UJT sweep circuit, VBB = 20V, VYY= 50V, R= 5KΩ, C= 0.01µF, η= 0.5
and Vv= 2V. Using the UJT characteristics, find
(a) the amplitude of sweep signal
(b) the slope and displacement error
(c) duration of the sweep
(d) the recovery time
Sol:
0.6 + 0.5* 20 = 10.6V
(a)Sweep signal amplitude:
Vs= Vp-Vv = 10.6V-2V = 8.6V

• Slope Error es =Vs/V
• V=peak to peak value of the sweep
• V= Vyy-Vv = 50-2=48V
• es =Vs/V = 8.2/48= 0.179
• Displacement Error ed= es/8=0.022
• Sweep time= Ts = RC ln (Vyy-Vv / Vyy-Vp ) = 9.87µs
• Recovery time=Tr= (2+5C)Vv= 4.1µs

Miller and Bootstrap Time base generators: basic Principles
• A simple exponential sweep generator is shown in figure, essentially
produces a non linear sweep voltage.

• In an exponential sweep generator, since the capacitor charges
exponentially, the resultant sweep generated is a non-linear one. To
get a linear sweep, the capacitor is required to charge with a
constant current.
• Let us consider the methods of linearizing an exponential sweep
• Introduce an auxiliary generator, v, as shown in Fig. 12.9(b).
• If v is always kept equal to the voltage across C(i.e.,v = vC), as the
polarities of v and vC are opposite, the net voltage in the loop is V.
Then i = V/R which is a constant.

• That means, the capacitor
charging current is constant
and perfect linearity is
achieved.
• Let us identify three nodes X,
Y and Z. In a circuit one
terminal, is chosen as a
reference terminal or the
ground terminal.Mr. M. Balaji, Dept. of ECE, SVEC 30

Miller integrator sweep generator
• Now let Z be the ground terminal
• The circuit can be redrawn as Fig. 12.10(b)

• Since v and vc are equal in
magnitude and opposite in
polarity, vi = 0.
• Hence, if the auxiliary
generator is replaced by an
amplifier with X and Z as
the input terminals and
Y and Z as output terminals
• then the gain A of the
amplifier should be infinity.
Replacing the auxiliary
generator by an amplifier
with gain infinity, the circuit
shown in Fig. 12.10(b) is
redrawn as that shown in
Fig. 12.10(c).Mr. M. Balaji, Dept. of ECE, SVEC 33

Slope error in Miller’s Sweep generator
• in which the auxiliary generator is replaced by an amplifier with gain
infinity.
• Thévenizing the circuit at the input, the Thévenin voltage source and
its internal resistance as V’ and R’

• As t → ∞, the capacitor is fully charged, hence, no current flows in
it. Thus, to calculate the output voltage, the capacitor can be
replaced by an open circuit. The resultant circuit is as shown in Fig.
12.11(c).
At t = ∞; vi=V’ 𝑖
Hence vo = AV’
We know that for an exponential sweep, es = Vs/V
Where Vs is the sweep amplitude and V is the peak to peak signal of
the output swing
In this case of miller’s sweep, the total peak to peak signal of the
output swing, vo = AV’, Hence

Even if Ri is small, as A is large, the slope error of a miller’s sweep is
very small. Hence, for all practical purposes this sweep generator
produces a near linear sweep.Mr. M. Balaji, Dept. of ECE, SVEC 41

Transistor miller time base generator:

•(vi) Calculation of the slope error: The slope error of the
Miller’s sweep generator is given by the relation:
where, Ri the resistance through which the capacitor charges
when the switch is OFF.
To calculate es, therefore, we have to calculate A and Ri of
the common-emitter amplifier.
The CE amplifier uses the h-parameter model as follows

Ri and A can be calculated using above equations and hence, the
value of es

Bootstrap Sweep Generators:
• Alternatively, in the circuit shown in Fig.
12.9(b) let Y be the ground terminal.
• The resultant circuit is shown in Fig.
12.13(a).
• Redrawing this circuit and replacing the
auxiliary generator by an amplifier with X
and Y as input terminals and Z and Y as the
output terminals, the amplifier should have a
gain of unity as v = vC, as shown in Fig.
12.13(b).

Replacing the generator by an amplifier, the circuit shown in Fig. 12.13(b) is redrawn as
shown in Fig. 12.13(c). The sweep generator represented in Fig. 12.13(c) is called a
bootstrap sweep generator because the increasing input at X is accompanied by an
identical rise in the output at Z, as the gain of the amplifier is unity

Slope error in Bootstrap Sweep generators:
• Consider the bootstrap sweep generator shown in Fig. 12.14(a) in
which the auxiliary generator is replaced by an amplifier with gain
1, which obviously is an emitter follower.
• If initially the capacitor is uncharged and if S is closed at t = 0, then
the voltage across C and Ri, i.e., vi = 0, Ri is replaced by a short
circuit. As vi = 0, Avi = 0 and is also replaced by a short circuit.

and as Ro of the emitter follower is very small, then vo ≈ 0.

Transistor bootstrap time-base generator

• A practical bootstrap ramp generator is shown in Fig. 12.16(a).
• The ramp is generated across capacitor C1 which is charged from the current
through R1.
• The discharge transistor Q1, when ON, keeps V1 at VCE(sat) until a negative
input pulse is applied.
• Q2 is an emitter follower with a low output resistance.
• Emitter resistance RE is connected to a negative supply (VEE) instead of
referencing it to the ground to ensure that Q2 remains conducting even
when its base voltage V1 is close to the ground.
• Capacitor C3, called the bootstrapping capacitance, has a much higher
capacitance than C1.
• C3 is meant to maintain a constant voltage across R1 and thus, maintain a
constant charging current .

(a) Quiescent conditions: The voltages under quiescent conditions (before the
application of a trigger) are calculated as illustrated below, using Fig. 12.16(b).

• When the input trigger signal is not present, Q1 has sufficient base current.
Therefore, Q1 is driven into saturation and the voltage V1 across the
capacitor C1 is VCE(sat). V1 = VCE(sat) (point X ), typically 0.2 V for Si, as
shown in Fig. 12.16(b). Q2 is an emitter follower for which input is V1 and its
output vo is:

(b) Sweep generation:
• At t = 0, as the trigger is applied,
the voltage at the base of Q1
goes negative, Q1 is OFF.
• The voltage at node K, VK = VCC +
V1 and D1 is OFF and is an open
circuit. The voltage at node X is
V1.

From Fig. 12.16(d), it is seen that
the output vo varies linearly only
when the duration of the gating
signal (Tg) is small so that in this
period vo does not reach VCC.
However, if Tg is large, the output
vo may reach VCC even before Tg.
When vo = VCC, the voltage VCE2 of
Q2 is practically zero (saturation).
Q2 no longer behaves as an emitter
follower. vo and V1 therefore remain
at VCC. The current VCC/R1 now
flows through C3, R1 and through
the base-emitter diode of Q2. Mr. M. Balaji, Dept. of ECE, SVEC 72

(c) Calculation of retrace time, Tr:
• At the end of the gate signal, at t = Tg, a current IB1 = (VCC/RB) again flows
into the base terminal of Q1. Q1 once again tries to go into saturation.
However, till such time VCE of Q1 is VCE(sat) (Q1 is in saturation), the collector
current, iC1 remains constant at
• As shown in Fig. 12.18, the current iR1 through R1 and the discharging
current id of C1 now constitutes iC1, the collector current of Q1, neglecting
the small base current IB2 of Q2,

Therefore V1 and vo fall linearly to the initial value.
The voltage variation during the retrace time Tr is:

• If the retrace time is large, it takes a longer time to initiate a new
sweep cycle. From Eq. (12.53), it is seen that RB will have to be small
to reduce the retrace time . However, if RB is too small, then the
collector current of Q1 becomes large as:
This results in greater dissipation in Q1. During the period, T = Tg + Tr, though
C3 is a large capacitor, it may still loose some charge. The circuit is said to
have recovered completely only when the charge lost by C3 is regained. The
minimum recovery time T1 for C3 can be found out as follows:

To reduce T1, VEE may be increased. However, this increases the quiescent
current in Q2 and hence, the dissipation in it

(d) Calculation of the slope error of a bootstrap sweep circuit:
• The slope error of the bootstrap, assuming that the charge on C3 remains
unaltered during the sweep duration, is given by the relation:
To calculate es, we have to
calculate A and Ri. For a common
collector amplifier we have:

For the Miller’s sweep circuit, VCC = 25 V, RC2 = 5 kΩ, RC1 = 10 kΩ.
The duration of the sweep is 5 ms. The sweep amplitude is 25 V.
Calculate (a) the value of C; (b) the retrace time and (c) the slope
error. The transistor has the following parameters: hfe = 80, hie = 1kΩ,
hoe = 1/40 kΩ and hre = 2.5 × 10−4.
• Sol: (a)

Time base Generators (part-1)

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