7.1 Explain what an operational amplifier (op amp) is - NSC Electrical Technology Power Systems - Question 7 - 2017 - Paper 1

1. Integrated circuits (ICs) are cheaper to manufacture due to mass production techniques, which reduce costs per unit.

2. ICs provide a compact solution, reducing the number of discrete components needed, which in turn simplifies circuit design and minimizes size.

A differential amplifier works by amplifying the voltage difference between two input signals while rejecting any signals that are common to both inputs. It uses two input terminals and outputs a voltage that is proportional to the difference between the inputs, typically expressed as:

$V_{out} = A_d (V_+ - V_-)$

where $A_d$ is the differential gain.

Negative feedback is commonly used in amplifier circuits to stabilize gain, improve bandwidth, and reduce distortion.

Positive feedback is employed in oscillator circuits to sustain oscillations and generate periodic waveforms.

Positive feedback amplifies the output by feeding a portion of it back to the input in phase, leading to increased gain and potential instability. In contrast, negative feedback reduces the output by feeding back a portion out of phase, which stabilizes gain and improves bandwidth.

To find the output voltage ($V_{out}$), we use the formula:

$V_{out} = (1 + \frac{R_f}{R_{in}}) \cdot V_{in}$

Substituting $R_f = 170 kΩ$, $R_{in} = 10 kΩ$, and $V_{in} = 0.7 V$:

$V_{out} = (1 + \frac{170000}{10000}) \cdot 0.7 = 12.6 V$

The voltage gain ($A_v$) can be calculated as:

$A_v = \frac{V_{out}}{V_{in}} = \frac{12.6}{0.7} = 18$. Hence, the voltage gain is -18 due to the inverting configuration.

1. Signal processing applications, such as audio mixing and filtering.

2. Measurement systems for gain control.

Monostable multivibrators are used in timer applications where a single output pulse is needed in response to a trigger input.

A monostable multivibrator has one stable state and produces a single output pulse in response to an input trigger. In contrast, a bi-stable multivibrator has two stable states and can hold either state indefinitely until it is triggered to switch states.

The input waveform for the integrator op amp will represent a ramp signal, leading to a triangular output waveform.

The input waveform for the inverting comparator will show the conditions of the input signals crossing the reference voltage, resulting in a square output waveform.

For the inverting Schmidt trigger, the input will show a sinusoidal waveform leading to a square wave output, influenced by upper and lower trigger levels.

The input waveforms will be combined, displaying each input waveform superimposed. The output waveform will show the sum of these inputs, typically with an inverted and scaled amplitude.

Given the input voltage $V_{in} = 5V$, we use the formula:

$V_{out} = - \frac{R_f}{R_{in}} \cdot V_{in}$

Substituting $R_f = 200 kΩ$, $R_{in} = 20 kΩ$:

$V_{out} = - \frac{200000}{20000} \cdot 5 = -50V$

The gain ($A_v$) is computed as:

$A_v = -\frac{R_f}{R_{in}} = -\frac{200000}{20000} = -10$. Hence, the gain is -10.

A common application of a Schmidt trigger is in signal conditioning to clean noisy signals by transforming inconsistent input signals into clean output pulses.

To calculate the resonant frequency ($f_0$):

$f_0 = \frac{1}{2 \pi \sqrt{L \cdot C}}$

Substituting $L = 27 mH$ and $C = 47 µF$:

$f_0 = \frac{1}{2 \pi \sqrt{(27 \times 10^{-3}) \cdot (47 \times 10^{-6})}} \approx 141.28 Hz$

The resonant frequency ($f$) is given by:

$f = \frac{1}{2 \pi RC}$

Substituting values $R = 25 kΩ$ and $C = 45 pF$:

$f = \frac{1}{2 \pi (25 \times 10^3)(45 \times 10^{-12})} \approx 57.76 kHz$