A triangular pulse is given at the input of an integrator circuit, the output will be of the form
Parabolic
An integrator raises the degree of its input by one, so a first-order ramp becomes a second-order curve.
The circuit relation :
\(V_{o}=-\dfrac{1}{RC}\int V_{in}\,dt\)
Now integrate a triangular wave. A triangle is made of straight-line segments, so on each segment the input is a linear function of time:
\(V_{in}=kt\qquad\Rightarrow\qquad V_{o}=-\dfrac{1}{RC}\int kt\,dt=-\dfrac{kt^{2}}{2RC}\)
The \(t^{2}\) is the answer: each segment produces a parabolic arc, and the output is a succession of parabolic curves — option 3.
The chain of waveforms is worth memorising, because these questions recur in both directions :
| Input | After integration | After differentiation |
|---|---|---|
| Impulse | Step | Doublet |
| Step | Ramp | Impulse |
| Square | Triangular | Impulses (spikes) |
| Triangular | Parabolic | Square |
| Sine | −Cosine (lags 90°) | Cosine (leads 90°) |
Option 1 is the trap for reading the table backwards : a square wave is what a triangle differentiates to, not what it integrates to. Option 2 would require the integrator to leave the waveform unchanged, which only happens for a sine wave (and even then the phase shifts by 90°).
Why the degree always rises by one. Integration is the inverse of differentiation, and each integration adds a power of t. A triangle is piecewise degree 1; its integral is piecewise degree 2, a parabola. Integrate again and the result is cubic.
Two practical points about the real circuit. First, a large resistor must be placed across the feedback capacitor, or the op-amp's input offset current will charge it steadily until the output saturates — the circuit then integrates only above \(f=\dfrac{1}{2\pi R_{sh}C}\). Second, the gain falls at 20 dB per decade, so an integrator attenuates high-frequency noise — the opposite of a differentiator, and the reason integrators rather than differentiators are used in analogue computing.
Hence, the output is parabolic.
Similar Questions
Assertion (A) : An Op-Amp is a direct coupled high gain amplifier.
Reason (R) : It consists of one or more differential amplifiers and usually followed by a level translator and push pull stage.
The input to a differentiator is –5 V. Its output will be
Match the following :
List – I List – II a. h-parameters i. O/P voltage varies as the slope of i/p voltage b. differentiator ii. Noise division c. half-wave rectifier iii. Function of a Q point d. integrator iv. series diode clipper Codes :
Assertion (A) : Op-Amp is used for sensor circuit.
Reason (R) : A small signal amplifier amplify weak measured signals.
Consider the following circuit, the switch S1 allows the output to switch between two ranges of amplitudes from 0-0.1 V and 0-1 V. Arrange these values of R1, R2 and R3 in increasing order.
(A) Value of R1
(B) Value of R2
(C) Value of R3Choose the most appropriate answer from the options given below :
The given operational amplifier circuit corresponds to which electronic circuit application ?
Statements in connection to Op-Amp applications are :
A. If we use a square wave generator followed by integrator circuit we get a triangular wave at the output
B. The logarithmic amplifier called a log-amplifier or a logger, is basically a current to voltage converter.
C.
is a first order high pass filter with voltage followerD. If we use a square wave generator followed by a clipping circuit then we get a saw-tooth wave generator.
Choose the correct answer from the options given below:
Match List I with List II
LIST I LIST II A. Single polarity positive voltage clipper circuit I. 
B. Negative clamping circuit II. 
C. Differentiator circuit III. 
D. Logarithmic Amplifier IV. 
Choose the correct answer from the options given below:
The correct flow in the basic block diagram of op-Amp is
A. Complementary symmetry push pull amplifier block.
B. Dual input unbalanced output differential amplifier block
C. Emitter follower with constant current source block
D. Dual-Input balanced output differential amplifier block
Choose the correct answer from the options given below :
Match the following :
List - I List - II a) 
i) 
b) 
ii) 
c) 
iii) 
d) 
iv) 
Codes :
Important Questions from Op-Amp and Its Applications
In the circuit shown below, $R$ is $1\text{ k}\Omega$ and $R_f$ is $10\text{ k}\Omega$. If $V_{\text{in}}$ is $100\text{ mV}$ and the op-amps have supply voltages of $\pm 15\text{ V}$, then $V_{\text{out}}$ is _______ V.
For IC 741 circuit shown below, the maximum input frequency above which the output will be distorted is ____________.
Assume that an op-amp 741 connected as a unit gain inverting amplifier is applied with an input change of 10 V. Determine the time taken for the output to change by 10 V. [Slew rate for op-amp 741 = 0.5 V/µs]
What is the value of output voltage $V_o$ in the given circuit? Assume op-amp to be ideal and MOSFET operating in saturation region.
In an ideal op-amp, the common mode gain is _____________.
