Oscillator Circuits: Feedback & Oscillation Conditions

Purpose of Oscillator Circuits

• An oscillator produces periodic waveforms with a DC supply voltage as its only input.
• Oscillators don't need repetitive input signals, except to synchronize oscillations sometimes.
• Output voltage can be sinusoidal or non-sinusoidal, based on oscillator type.
• Two main types are feedback oscillators and relaxation oscillators.

Feedback Oscillators

• The feedback oscillator returns a fraction of the output signal to the input without any net phase shift.
• This results in reinforcement of the output signal.

Conditions for Oscillation

• Barkhausen stability criterion is a mathematical condition determining when a linear electronic circuit oscillates.
• For sustained oscillation:
  • The phase shift around the feedback loop must be 0° or a multiple of 2π.
  • The voltage gain (Acl) around the closed feedback loop (loop gain) must equal 1 (unity).
• Voltage gain around the closed feedback loop (Acl) equals amplifier gain (Av) times feedback circuit attenuation (B): Acl = AvB.
• A loop gain greater than 1 rapidly saturates the output, creating unacceptable distortion when a sinusoidal wave is desired.
• Gain control maintains a loop gain of 1 to prevent distortion.
• If feedback circuit attenuation is 0.01, the amplifier needs a gain of 100 to avoid distortion (0.01 × 100 = 1.0)
• Amplifier gain beyond 100 causes waveform peaks to be limited

Positive Feedback

• Positive feedback involves feeding an in-phase portion of the amplifier's output voltage back to the input with no net phase shift.
• This reinforces the output signal.
• In-phase feedback voltage (Vf) gets amplified to produce the output voltage, which in turn regenerates the feedback voltage, creating a self-sustaining signal loop.
• The self-sustaining signal loop and continuous sinusoidal output is known as oscillation.
• Most amplifiers have a 180° phase change.
• An additional 180° phase change is needed to achieve the required zero net phase shift.

The Phase-Shift Oscillator

• A phase-shift oscillator is a type of sinusoidal feedback oscillator.
• Each of the three RC circuits in the feedback loop provides a maximum phase shift approaching 60°.
• Oscillation happens where the total phase shift via the three RC circuits totals 180°.
• The amplifier's inversion adds the remaining 180° to meet the 360° (or 0°) phase shift requirement around the feedback loop.

The Colpitts Oscillator

• The Colpitts oscillator is a resonant circuit feedback oscillator.
• It uses an LC circuit, acting as a resonant filter to pass the desired oscillation frequency and supply phase shift.
• Oscillation frequency approximates the resonant frequency of the LC circuit.
• The values of C1, C2, and L establish the oscillation frequency.
• It's name begin's with a "C," and the circuit uses split capacitors.

The Hartley Oscillator

• The Hartley oscillator resembles the Colpitts, but the feedback circuit has two series inductors and one parallel capacitor.

The Armstrong Oscillator

• The Armstrong oscillator uses transformer coupling to feed back part of the signal voltage.
• It uses a transformer secondary, or "tickler" coil, to provide feedback for sustained oscillation.
• Armstrong oscillators are less common than Colpitts and Hartley due to transformer size and cost issues.
• Primary winding inductance (Lpri) in parallel with C₁ sets the oscillation frequency.

Crystal-Controlled Oscillators

• Crystal-controlled oscillators are the most stable and accurate feedback oscillator type.
• They utilize a piezoelectric crystal in the feedback loop to manage frequency.

The Piezoelectric Effect

• Quartz shows the piezoelectric effect.
• Mechanical stress applied to a crystal causes a voltage to develop at the mechanical vibration frequency.
• AC voltage applied to a crystal makes it vibrate at the applied voltage's frequency.
• The biggest vibration occurs at the crystal's inherent resonant frequency, based on its physical size and cut.
• Electronic application crystals usually have a quartz wafer between two electrodes inside a protective enclosure.
• A crystal's schematic symbol equates to a series-parallel RLC circuit.
• Crystals operate in series or parallel resonance.
• At series resonance, inductive reactance cancels Cs reactance; the remaining Rs determines crystal impedance.
• Parallel resonance arises when inductive reactance and parallel capacitance (Cm) reactance become equal.
• Parallel resonance frequency typically exceeds series resonance by at least 1 kHz.
• Crystals have very high Q factors
• Q factors exceeding 10^6 are easily achievable, ensuring <1 part per million accuracy in strict lab conditions.

Crystal Oscillators in Circuits

• An oscillator using a series resonant tank circuit has minimum crystal impedance at the series resonant frequency, maximizing feedback.
• The crystal tuning capacitor (Cc) finely adjusts the oscillator frequency by manipulating crystal resonance.
• A modified Colpitts configuration uses a crystal as a parallel resonant tank circuit, where impedance is highest at parallel resonance, maximizing voltage across the capacitors.
• C₁ voltage is fed back to the input.

Relaxation Oscillators

• Relaxation oscillators use an RC timing circuit to create a waveform.
• The waveform is typically a square wave or other non-sinusoidal waveform.
• A Schmitt trigger alternates the charging and discharging of a capacitor.

Relaxation Oscillator Operation

• Initially, C₁ is discharged, setting node 1 at 0 V.
• Q2's base-emitter is reversed biased (Q2 base at Vdd/2 and emitter at 0 V), so Q2 doesn't conduct.
• Because Q2 is open, Q₁ gets no base current and doesn't conduct.
• C₁ voltage increases while charged by current from the power supply through R4.
• At node 1, voltage rises exponentially as C₁ charges.
• When C₁ voltage reaches Q2's emitter-base forward bias voltage (Vdd/2 + 0.7 V), Q2 starts conducting.
• Q1 then gets base current through Q2, starts conducting, and pulls Q2's base low.
• The capacitor C₁ discharges quickly across the BJT combination because R3 has a low value
• Voltage at junction 2 doesn't drop to 0 V.
• When C₁ voltage drops below 0.7 V, Q2 stops conduction, and the BJT disengages, C₁ charges again via R4.
• The node 2 voltage becomes Vdd/2.
• R3 adjusts pulse width at junction 2.
• Increased R3 widens the pulses.
• Increasing R4 or C₁ reduces frequency (similar to boosting the power supply).
• R3 controls the reset timing for generated ramp waveforms.

Astable Multivibrator

• An astable (no-stable-state) multivibrator oscillates freely.
• Free running means it oscillates between two distinct output voltage levels for a set time.
• Each output level holds for a specific duration.
• The astable multivibrator has two outputs and generates continuous square or rectangular waves on an oscilloscope.

Astable Multivibrator Circuit Analysis

• Approximately all of the circuit's current flows through Q1, which provides virtually no resistance to current flow.
• Capacitor C₁ charges.
• Q₁ has nearly zero resistance in its saturated state; C₁ charges at a rate based on the time constant of R2 and C₁ (TC = RC).
• Capacitor C₁'s right-hand side is connected to transistor Q2's base, which is now at cut-off.
• Capacitor C₁'s right-hand side is becoming increasingly negative.
• Q2 conducts if the base becomes sufficiently negative.
• Q2 will change states from cut-off to conduction following a period.
• R2C1 determines the time taken for Q2 to saturate.

Monostable Multivibrator

• Also known as a one-shot multivibrator.

Monostable Multivibrator Circuit Analysis

• Initially, Q1 is cut off, so there is no current through R₁, and the collector of Q1 is at -VCC.
• Q2 is saturated with near 0 voltage drop, so its collector is near 0 volts.
• The base of Q1 is positive due to the voltage division between R5 and R3 from VBB to ground at the collector of Q2.
• Thus, the base of Q1 is maintained positive.
• Since the Q2's base is slightly negative from the voltage drop across R2, Q2 stays saturated.
• If the collector of Q1 is close to -Vcc and the base of Q2 is close to ground, C₁ should be charged to almost vcc volts.
• By inserting a negative pulse at the input terminal, one can see how the circuit works.
• C2 transmits the voltage change to Q1's base, turning Q₁ on.
• Q₁ quickly saturates, and Q1's collector voltage immediately goes to ground.
• Base of Q2 causes Q2 to cut off because of this significant voltage increase transmits through C₁ due to coupling; At this point, Q2 collector voltage falls instantly to Vcc.
• Created voltage divider by R5 and R3 now maintains a negative base for Q₁, which is locked.
• The system only activates once the pulse has been passed as the Q₁ base holds the circuit cannot be turned off.
• Note that the base of Q2 is connected to C₁, which keeps the positive charge that keeps Q2 off. In essence, coupling with a positive voltage change happens from with Q₁ starts conducting.
• The collector for Q1 switches between -Vcc volts and 0 volts, so the charge for C₁ acts as a battery.
• The Q2 voltage shorts and runs through, -Vcc, through R2 on one side of C1.

Bistable Multivibrator

• As its name hints, the bistable multivibrator features two stable states.
• With sufficient amplitude, it modifies states upon receiving the right polarity trigger until set off again.
• Trigger requirements can be met from different sources that are not fixed via Pulse Repetition Frequency (PRF).

Flip-Flop Circuit

• A bistable multivibrator is commonly called a flip-flop or Eccles-Jordan circuit.
• "bi" (two) implying two steady states are present in the flip-flop,
• If connected to the output and had a device, it would read a zero voltage (low) or small positive or negative value.
• Remember, stable implies state retention of a flip-flop
• It will not change until a correct trigger comes in.
• Two outputs and two inputs are present on the example flip-flop shown, whereas transistors connect to bases with two output couplings.

Flip-Flop Circuit Diagram

• A standard block diagram is shown.
• Inputs (S for set, and C for clear from left) while outputs get shown on the right with 1 and 0 for a flip-flop.
• Based upon the transistor kind, an applied impulse yields to output 1 from which a positive may result given which 0 volts result at the 0 output.
• An impulse sent yields to 0 outputs which may have a resulting positive or a negative voltage. Which results with the "clear state:"