Operational Amplifiers and Output Devices in Electronics

Electronics: Operational Amplifiers and Output Devices

21.1 The Ideal Operational Amplifier

Operational amplifiers (op-amps) are fundamental components in analog electronic circuits, designed to amplify voltage differences between two inputs. An ideal op-amp is a theoretical model used to simplify analysis and design.

• Infinite Input Impedance ($Z_{in}$): Prevents any current from flowing into the amplifier's input, ensuring no loading of the source.

• Infinite Open Loop Voltage Gain ($A$): The amplifier can amplify even the smallest voltage difference between its inputs.

• Zero Output Impedance ($Z_{out}$): Ensures all output voltage is delivered to the load without loss.

• Infinite Bandwidth (BW): Can amplify signals of any frequency without attenuation.

• Infinite Slew Rate: No delay between input changes and output response.

Example: In practice, these ideal properties are approximated but not fully realized in real op-amps.

21.1.1 The Real Op-Amp

Real operational amplifiers deviate from the ideal model due to physical limitations:

• Input Impedance: Typically between $10^6$ and $10^{12}~\Omega$.

• Open Loop Gain: Usually around $10^5$ for DC voltages.

• Output Impedance: Not zero, but typically about $10^2~\Omega$.

• Bandwidth: Limited; cannot amplify all frequencies equally.

• Slew Rate: Finite, e.g., $10~\text{V}~\mu\text{s}^{-1}$.

21.1.2 Output Voltage of an Op-Amp

The output voltage of an op-amp is proportional to the difference between the non-inverting ($V^+$) and inverting ($V^-$) inputs, multiplied by the open-loop gain ($A_0$):

$V_{out} = A_0 (V^+ - V^-)$

However, the output cannot exceed the supply voltages; if it does, the amplifier is said to be saturated.

21.1.3 Power Supply and Reference Line

Op-amps require both positive and negative supply voltages. The common or earth line serves as a reference for all input and output voltages, allowing the output to swing both positive and negative relative to this reference.

21.2 Operational Amplifier Circuits

Op-amps can be configured in various ways to perform different functions, such as amplification, comparison, and signal processing.

21.2.1 Op-Amp as a Comparator

An op-amp can compare two voltages and output a high or low voltage depending on which input is greater. There is no feedback in this configuration:

$V_{out} = A_0 (V^+ - V^-)$

If $V^+ > V^-$, output is positive (saturated at supply voltage); if $V^+ < V^-$, output is negative (saturated at negative supply voltage).

21.2.2 Feedback in Op-Amps

Feedback involves returning a portion of the output to the input. It can be positive or negative:

• Negative Feedback: Reduces gain but increases bandwidth, reduces distortion, and improves stability.

The overall voltage gain with feedback ($\beta$ is the feedback fraction):

$V_{out} = \frac{A_0}{1 - A_0 \beta} V_{in}$

21.2.3 The Inverting Amplifier

In this configuration, the input signal is applied to the inverting input, and the non-inverting input is grounded. The output is inverted and scaled by the ratio of two resistors:

$A_0 = -\frac{R_f}{R_{in}}$

$V_{out} = -\left(\frac{R_f}{R_{in}}\right) V_{in}$

Example: For $R_f = 22~k\Omega$, $R_{in} = 10~k\Omega$, $V_{in} = 0.44~V$:

$V_{out} = -\left(\frac{22}{10}\right) \times 0.44 = -0.968~V$

21.2.4 The Non-Inverting Amplifier

Here, the input is applied to the non-inverting input. The output is in phase with the input and the gain is always greater than one:

$A_0 = 1 + \frac{R_f}{R_{in}}$

$V_{out} = \left[1 + \left(\frac{R_f}{R_{in}}\right)\right] V_{in}$

Example: For $R_f = 10~k\Omega$, $R_{in} = 2~k\Omega$, $V_{in} = 0.20~V$:

$A_0 = 1 + \frac{10}{2} = 6$ $V_{out} = 6 \times 0.20 = 1.2~V$

21.2.5 Applications and Examples

• Light-dependent resistor (LDR) circuits for sensing light intensity.

• Use of op-amps in microphone amplifiers and sensor signal conditioning.

21.3 Output Devices

Output devices convert the processed electrical signal into a usable form, such as light, sound, or a display reading.

• Relay: An electromagnetic switch that allows a small current to control a larger current.

• Light-Emitting Diode (LED): Emits light when forward biased; used as indicators or in sensing circuits.

• Digital and Analogue Meters: Display voltage, current, or other quantities as output.

Sensing Devices

• LDR (Light Dependent Resistor): Resistance decreases with increasing light intensity.

• Thermistor: Resistance changes with temperature.

• Piezo-electric Transducer: Produces voltage in response to sound pressure.

• Strain Gauge: Resistance changes with mechanical strain.

Direct Sensing

Direct sensing involves converting a physical property (e.g., light, temperature) into an electrical signal using a sensor. The signal is then processed and sent to an output device.

Example: An LDR senses light intensity, the signal is amplified by an op-amp, and the output device (e.g., LED) indicates the result.

Table: LED Response in Comparator Circuit

$V_{IN}$ / V	Red LED	Green LED
+2.0	✓ ($V^+ > V^-$)	✗ ($V^+ < V^-$)
+4.0	✓ ($V^+ > V^-$)	✗ ($V^+ < V^-$)
+6.0	✓ ($V^+ > V^-$)	✗ ($V^+ < V^-$)

Additional info: The table shows which LED is on depending on the input voltage compared to a reference voltage.

Summary

• Operational amplifiers are versatile components used for amplification, comparison, and signal processing in electronics.

• Ideal op-amps have infinite gain, input impedance, bandwidth, and zero output impedance, but real op-amps approximate these properties.

• Feedback, especially negative feedback, is crucial for stable and predictable amplifier operation.

• Op-amps are used in various sensor and output device circuits, forming the basis of many electronic measurement and control systems.