An oscillator is an electronic circuit that generates a repetitive, oscillating electronic signal, often a sine wave or a square wave, without the need for an external input signal. Oscillators are fundamental components in almost all electronic systems, used in clocks, timers, radio frequency circuits, signal generators, and many other applications.

Basic Principle of Oscillation (Barkhausen Criteria): For sustained oscillations to occur in an amplifier circuit with feedback, two conditions, known as the Barkhausen Criteria, must be met:
1. Loop Gain Magnitude Condition: The magnitude of the loop gain (Aβ) must be equal to or greater than unity (1). |Aβ|≥1 Where 'A' is the gain of the amplifier stage and 'β' is the gain of the feedback network. In practice, the loop gain must be slightly greater than 1 to ensure oscillations start and reach a stable amplitude, after which a non-linear mechanism (e.g., amplifier saturation) brings the effective loop gain down to exactly 1.
2. Phase Shift Condition: The total phase shift around the feedback loop must be 0° or an integer multiple of 360°. ∠Aβ=0° or n·360° (where 'n' is an integer). This means the feedback signal must be in phase with the input signal to reinforce it.

Oscillators are broadly classified into two main types:
● Sinusoidal (Linear) Oscillators: Produce a sine wave output. They typically use a frequency-selective feedback network (like an RC or LC circuit) to determine the oscillation frequency. Examples include Wien Bridge, Hartley, Colpitts, Phase-Shift oscillators.
● Relaxation Oscillators: Produce non-sinusoidal waveforms like square waves, triangular waves, or sawtooth waves. They typically use timing circuits (e.g., RC circuits) and switching devices.

The Wien Bridge oscillator is a very popular and stable low-frequency (typically 1Hz to 1MHz) sinusoidal oscillator. It is often implemented using an Operational Amplifier (Op-Amp) as the active gain element.

Circuit Configuration: The Wien Bridge oscillator consists of two main parts:
1. A positive feedback network: This is a series RC circuit in parallel with another parallel RC circuit. This forms a lead-lag network. At a specific frequency, this network provides a phase shift of 0° and a voltage gain of 1/3.
2. An Op-Amp amplifier: Configured as a non-inverting amplifier. This amplifier provides the necessary gain to compensate for the attenuation in the feedback network and meet the Barkhausen criteria. For the loop gain to be at least 1, the Op-Amp's gain must be at least 3.

Conditions for Oscillation:
● Phase Shift: The Wien Bridge network has a phase shift that varies with frequency. At the resonant frequency (f0), the phase shift of the network is exactly 0°. This satisfies the phase condition.
● Gain: At f0, the voltage gain of the Wien Bridge network is 1/3. Therefore, for sustained oscillations (|Aβ|≥1), the Op-Amp amplifier must provide a gain (AV) of at least 3. For a non-inverting Op-Amp amplifier, AV = 1 + Ri/Rf. So, 1 + Ri/Rf ≥3 ⟹ Ri/Rf ≥2. A common choice is to set Rf = 2Ri.

Oscillation Frequency (f0): If the resistors and capacitors in the Wien Bridge network are chosen such that R1 = R2 = R and C1 = C2 = C, then the oscillation frequency is given by: f0 = 2πRC1.

Amplitude Stabilization: In a practical Wien Bridge oscillator, a method for amplitude stabilization is often used. If the gain is too high, the output waveform will clip. If it's too low, oscillations will die out. A common technique is to use a non-linear element in the feedback path of the Op-Amp, such as:
● Diodes: Two back-to-back zener diodes or signal diodes can clip the output if the amplitude exceeds a certain level, effectively reducing the loop gain at high amplitudes.
● Light Dependent Resistor (LDR) or Thermistor: These components' resistance changes with light intensity or temperature. By incorporating them into the Op-Amp's gain-setting feedback network, the gain can be adjusted dynamically to maintain a stable output amplitude.

LC oscillators use a tuned LC (Inductor-Capacitor) circuit to determine the oscillation frequency. They are generally used for higher frequencies (RF applications) compared to RC oscillators. The LC tank circuit acts as the frequency-selective feedback network, and the active element can be a BJT, FET, or Op-Amp (though Op-Amps are limited to lower RF due to bandwidth).

General Principle of LC Oscillators: The LC tank circuit has a resonant frequency at which it stores energy and oscillates. The active device (e.g., BJT) provides the necessary gain and compensates for losses in the tank circuit, ensuring continuous oscillations. The feedback is provided from the tank circuit back to the active device.

Configuration: The Hartley oscillator uses a tapped inductor or two inductors in series (L1, L2) and a single capacitor (C) in the tank circuit. The feedback is provided from the junction of the two inductors.

Principle: The feedback voltage is developed across one part of the tapped inductor (L1 or L2) and applied to the active device's input (e.g., base of BJT, gate of FET). The output is taken across the entire tank or the other part of the inductor. The 180° phase shift required for oscillation is provided by the amplifier and the inductive coupling.

Configuration: The Colpitts oscillator uses a single inductor (L) and a tapped capacitor or two capacitors in series (C1, C2) in the tank circuit. The feedback is provided from the junction of the two capacitors.

Principle: Similar to Hartley, but here the feedback voltage is developed across one of the capacitors (C1 or C2). The output is taken across the entire tank or the other capacitor.

Oscillation Frequency (f0): f0 = 2πLCeq1, where Ceq is the series combination of C1 and C2: Ceq = C1 + C2 C1 C2. So, f0 = 2πL(C1 + C2/(C1C2)).

A current mirror is a circuit designed to copy a current through one active device to another active device, thereby 'mirroring' the current. It is used to create stable and predictable DC currents in integrated circuits and discrete designs. Current mirrors are essential for biasing amplifiers, active loads, and differential pair circuits.

Basic Principle: The operation relies on the matched characteristics of two (or more) transistors (BJTs or FETs) and the fundamental relationship between their control voltage (VBE for BJTs, VGS for FETs) and their output current. If two identical transistors have the same control voltage, they will ideally conduct the same current.

Key Performance Metrics:
● Current Matching Accuracy: How closely the output current matches the reference current. Affected by transistor matching, Early effect, and base currents (for BJTs).
● Output Resistance (Rout): How well the output current remains constant despite changes in the load voltage (collector-emitter voltage for BJT, drain-source voltage for FET). A higher output resistance indicates better current source behavior.
● Minimum Operating Voltage: The minimum voltage required across the output transistor to keep it in the active/saturation region.

Configuration: A simple BJT current mirror consists of two matched NPN (or PNP) transistors, Q1 and Q2.
● Q1 is configured as a diode: its collector is shorted to its base. This forces Q1 into active region operation (or saturation if base current is too high, but usually active).
● A reference current (IREF) flows into the collector of Q1. This current is set by a voltage source (VCC) and a reference resistor (RREF).
● The base of Q1 is connected to the base of Q2. Since the transistors are matched, VBE1 = VBE2.
● The emitters of both Q1 and Q2 are connected to ground.
● The output current (IOUT) is taken from the collector of Q2, flowing into a load.

Limitations of Simple Current Mirror:
● Base Current Error: A portion of IREF is consumed by the base currents of Q1 and Q2. IREF = IC1 + IB1 + IB2 = IC1 + βIC1 + βIC2. If IC1 = IC2 = IC, then IREF = IC(1 + 2/β). So, IOUT = IC = (1 + 2/β)IREF. The output current is actually slightly less than IREF. This error is significant if β is low.
● Early Effect: As the collector-emitter voltage of Q2 (VCE2) changes (due to varying load resistance), its collector current (IC2) will change slightly due to the Early effect (base width modulation). This means the output current is not perfectly constant, and the output resistance is limited. The output resistance Rout of the simple current mirror is approximately the output resistance of the transistor itself, ro = IC/VA + VCE, where VA is the Early voltage.

Wilson Current Mirror: Improves current matching accuracy and significantly increases output resistance. It uses three transistors, effectively reducing the base current error and mitigating the Early effect by keeping the VCE of the mirroring transistor (Q2) more constant. Its output resistance is roughly βro, much higher than the simple mirror.

Widlar Current Mirror: Designed to generate very small output currents (much smaller than IREF) which are difficult to achieve with a simple mirror using large resistors. It achieves this by adding a resistor in the emitter of the output transistor. This creates a small VBE difference between the two transistors, allowing for very low output currents. However, its output resistance is similar to the simple current mirror.