RF Circuits and Systems - Oscillators

- Applying the oscillation condition, called Barkhausen Criteria, to derive the minimum required gain and the oscillation frequency of the three-stage ring oscillator, where each delay stage is a comm-source

- Investigating the oscillator's behavior for various configurations of the poles and zero of the closed-loop transfer function

- Examining the "gain-control mechanism" in an oscillator that helps producing the sustainable oscillation.

- Studying the widely used ring oscillator where each stage is a complementary NMOS-PMOS stage.

-Calculating the oscillation frequency based on the signal transition.

- Large-signal study of a ring oscillator's behavior

- Differential ring oscillator

- large-signal analysis of the differential ring oscillator

- Introducing several differential delay stages for differential ring oscillator

- Exploring the pole-zero configuration of the closed-loop system in oscillatory behavior

- Analysis of root-locus of a unity-gain feedback system in oscillation with an open-loop stage having simplest pole-zero pattern

- Calculating the minimum required gain and oscillation frequency of a closed-loop circuit having an open-loop stage with a pair of poles and a zero

- An overview of the root locus analysis of the closed-loop feedback network incorporating an open-loop circuit with two poles and one zero in the left half plane.

- Studying the open-loop circuit with a complexity conjugate left-half plane poles.

- Circuit realization:

    1. Realization of the open-loop circuit using an RLC tank circuit

    2. Building the unit-gain feedback network around the RLC tank

    3. Putting them all together and using the transistor to close the loop

- Transformer-feedback LC oscillators

- How does inductor's loss change the dynamic of the LC circuit?

- Defining the circuit's quality factor

- The analysis of the LC circuit accounting for the series loss

- Introducing the series-to-parallel and parallel-to-series transformation methods.

-Examining the single-tuned amplifiers

- Revisiting the feedback network using a tuned amplifier in the feedforward path

- Step-by-step analysis of the cross-coupled pair LC oscillators

- Cross-coupled pair showing negative resistance

- Revisiting transformer feedback LC oscillators

- Studying the capacitive voltage division network as a transformer in a tank circuit

- Building the Colpitts oscillator

- Introducing a fundamental composite circuit playing as a foundation for Pierce, Clapp, and Colpitts oscillator topologies

Going over two problems in great detail:

1. A problem on a differential ring VCO

2. A two-part problem on LC oscillators

- An overview of the fundamental composite cell exhibiting a negative resistance

- Quadrature LC oscillators

- Studying the conditions to generate in-phase and anti-phase couplings for two oscillators coupled together.

- A brief look at the injection locking, and its use to calculate the oscillation frequency of a quadrature LC oscillator

- Presenting the concept of the voltage-controlled oscillator

- Introducing the important design specs

- Tuning mechanisms in ring oscillators

- Investigating the advantages and disadvantages of a multi-stage differential ring oscillator where each delay stage in a differential NMOS pair with PMOS loads in triode

- Presenting a delay stage that mitigates the non-constant oscillation amplitude problem of the differential delay stage with PMOS loads.

- Studying a delay stage employing a main resistively loaded differential pair and a cross-coupled pair whose current is controlled by a control voltage

- Investigating the problems of the above delay stage and finding circuit level solutions.

- Studying a tuning technique based of the deal;y interpolation

- Building the delay circuit based on this idea and developing a ring VCO based on this delay stage

- Studying the tuning in LC oscillators

- Starting with a junction capacitance and placing it alongside the LC oscillators

- Introducing the MOS varactor

- Presenting the varactor-based LC VCO incorporating a complementary NMOS-PMOS cross-coupled pairs

- Discrete tuning in LC VCO's

- Inductive tuning in LC oscillators and studying two techniques to achieve inductive tuning

      1. Magnetic coupling

      2. Active inductors

- On-chip inductor structures

- An overview of planar spiral inductors

- Lumped circuit model of the spiral structures

- A general overview of phase noise in oscillators

- Definitions

- An LT approach modeling the phase noise

- Reviewing the Leeson Formula