Unit 3: Amplifiers, Oscillators and Operational Amplifiers
1. Hybrid Parameter (h-parameter) and Equivalent Circuit
Hybrid parameters, or h-parameters, are used to represent a transistor as a two-port network for small-signal AC analysis. They are called "hybrid" because they use a mixture of units (Ohms, Mhos, and unitless ratios).
The four h-parameters for a Common Emitter (CE) configuration are:
- hie: Input impedance (Ohms).
- hre: Reverse voltage gain (unitless).
- hfe: Forward current gain (unitless).
- hoe: Output admittance (Mhos).
2. Analysis of CE Amplifier using h-parameters
Using the h-parameter equivalent circuit, we can derive expressions for the performance of a CE amplifier:
- Current Gain (Ai): The ratio of output current to input current.
- Voltage Gain (Av): The ratio of output voltage to input voltage.
- Input Impedance (Zi): The resistance seen by the input signal.
- Output Impedance (Zo): The resistance seen looking back into the output terminals.
3. Frequency Response of Two-Stage R-C Coupled Amplifier
In multi-stage amplifiers, stages are connected via a capacitor and a resistor (R-C coupling).
The frequency response is a plot of voltage gain versus frequency. It remains constant over a specific range called the Bandwidth (BW). Gain drops at low frequencies due to coupling capacitors and at high frequencies due to internal transistor capacitances.
4. Sinusoidal Oscillators and Barkhausen's Criterion
An oscillator is a circuit that produces a continuous, periodic output signal without an external input.
For self-sustained oscillations, the Barkhausen's Criterion must be satisfied:
1. The loop gain (product of amplifier gain A and feedback fraction β) must be equal to unity: |Aβ| = 1.
2. The total phase shift around the loop must be 0° or 360°.
5. RC Phase Shift Oscillator
The RC Phase Shift Oscillator uses an RC network in the feedback loop to provide the required 180° phase shift. Since the CE amplifier already provides 180°, the total loop phase shift becomes 360°.
The frequency of oscillation is determined by the R and C values in the feedback network.
6. Operational Amplifiers (IC-741): Characteristics
An Operational Amplifier (Op-Amp) is a high-gain DC-coupled electronic voltage amplifier with differential inputs. The IC-741 is the most common practical Op-Amp.
Key Parameters:
- CMRR (Common Mode Rejection Ratio): Ability to reject signals common to both inputs.
- Slew Rate: Maximum rate of change of output voltage per unit time.
- Virtual Ground: A concept where the inverting terminal is at zero potential if the non-inverting terminal is grounded, provided the open-loop gain is infinite.
7. Applications of Op-Amp
By using different feedback networks, Op-Amps can perform mathematical operations:
- Adder (Summing Amplifier): Produces an output proportional to the sum of input voltages.
- Differentiator: Produces an output proportional to the rate of change of the input voltage.
- Integrator: Produces an output proportional to the integral of the input voltage over time.
- Inverting/Non-inverting Amplifiers: Basic configurations for signal amplification.
Exam Focus Corner
Frequently Asked Questions
- State the ideal characteristics of an Op-Amp.
Infinite gain, infinite input impedance, zero output impedance, infinite bandwidth, and infinite CMRR.
- Why is the RC Phase Shift Oscillator used for low frequencies?
Because at high frequencies, the size of capacitors required becomes too small, making the circuit unstable.
Common Mistakes
- Virtual Ground: Applying the "Virtual Ground" concept to non-inverting configurations. It only applies to the inverting input when the non-inverting input is grounded.
- Oscillators: Confusing the phase shift of the amplifier with the phase shift of the feedback network. Both must sum to 360°.
Exam Tips
Tip: When deriving Op-Amp formulas (Adder/Integrator), always start by stating that the input current to the Op-Amp is zero due to infinite input impedance. This simplifies the Kirchhoff’s Current Law (KCL) analysis at the inverting node.