Oscillator Simulation and Design

Today we explore the use of oscillator synthesis software (Genesys) for practical crystal oscillator design, and the impact of the Randall-Hock correction formula on linear open loop analysis accuracy.

References and additional reading:

Description Reference
Oscillator synthesis/simulation software Genesys, Keysight Technologies
Randall and Hock’s IEEE paper (no paywall) General oscillator characterization using linear open-loop S-parameters, Mitch Randall, Terry Hock
Application of the Randall-Hock correction formula in oscillator synthesis Discrete Oscillator Design, Chapter 1.2.1.5, Randall W. Rhea
Randall Rhea’s oscillator design webinar Discrete Oscillator Design Tools and Techniques, Randall W. Rhea, presented by Keysight Technologies
Effects of S11 and S22 on oscillator loop gain Practical RF Circuit Design for Modern Wireless Systems, Vol. 2, Chapter 6.2, Rowan Gilmore, Les Besser
Evaluating and optimizing oscillator performance using Genesys simulation Improving the Vackar Oscillator, QRP Quarterly, Volume 56 Number 1, January 2015, p.20, David White (WN5Y)

A 100kHz Zero Droop Peak Detector

Here’s an inexpensive precision peak detector circuit that accurately tracks the peak voltage of input signals at frequencies up to 100kHz and has zero voltage droop over an indefinite period of time…no microcontrollers required!

The following circuit uses a dual comparator, three op amps, and a digital potentiometer to provide two peak detection outputs: one “real-time” peak output, accurate to within 2% for input signals up to 100kHz, and one maximum peak output which outputs the maximum peak voltage seen since the last reset:

Precision zero-droop 100kHz peak detector circuit

Precision zero-droop 100kHz peak detector circuit

References and additional reading:

Description Reference
A comparator based peak detector LM311 Datasheet, Texas Instruments, Figure 28
A droopless peak detector using a digital potentiometer Application Note 1163, Maxim Inetgrated
Wide bandwidth precision peak detector Precision Peak Detector Uses No Precision Components, Jim McLucas, EDN
High speed peak detector design Peak Detectors Gain in Speed and Performance, John Wright, Linear Technologies, Design Note 61

Single Supply Op-Amp Rectifiers

An introduction to single-supply precision op-amp rectifier circuits, their inherent limitations, and a single-supply design that outperforms even its dual-supply counterparts!

Single supply full wave rectifier with wide dynamic range and low distortion to >20kHz

Single supply full wave rectifier with wide dynamic range and low distortion to >20kHz

References and additional reading:

Description Reference
Basic single supply full wave rectifier circuit LT1078 Absolute Value Circuit (Full-Wave Rectifier), Linear Technologies
Improved single supply full wave rectifier Burr-Brown Application Bulletin: Precision Absolute Value Circuits, David Jones & Mark Stitt
High speed (500kHz) full wave rectifier Intersil Application Note 1698, Tamara Schmitz
High speed (2.5MHz) precision rectifier High Speed Comparator Techniques (Application Note 13), Jim Williams

Precision Op-Amp Rectifiers

An introduction to using operational amplifiers for precision half-wave and full-wave rectification of AC signals: How it works, how to configure the circuits for gain/attenuation, and the effects of op-amp slew rate and resistor matching on the precision of the rectified signal.

Single OpAmp Window Comparators

A recent question on the Electrical Engineering Stack Exchange site got me thinking about some interesting window comparator circuits. Here’s how to detect three different input voltage levels with just one op-amp!

References and additional reading:

Description Reference
Simplified window comparators Applications of Operational Amplifiers, Third-Generation Techniques, Jerald G. Graeme, Chapter 4.1.2
Tri Level Voltage Detector LVM821 Datasheet, Texas Instruments, Section 8.2.3

The RC Filter Transfer Function

Most people are familiar with the simple first-order RC low pass filter:

RC Low Pass Filter

Also well known is the equation for calculating the -3dB (aka, half-power) cutoff frequency of the RC low pass filter:

\(
\begin{equation}
\mathbf{f}_{c} = \frac{1}{2 \pi RC}\\
\end{equation}
\)

It’s an easy equation to memorize, but if you’re interested in where this equation comes from, read on; if you’re familiar with resistor voltage dividers, this will be a piece of cake!

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Colpitts Crystal Oscillator Design

A qualitative and quantitative analysis of the Colpitts crystal oscillator circuit, oscillation requirements, and practical circuit design considerations.

References and additional reading:

Description Reference
Quantitative analysis of Colpitts crystal oscillators Crystal Oscillator Design and Temperature Compensation, Marvin E. Frerking, Chapter 7.3, Appendix F
Oscillator phase vs frequency, and crystal loaded Q analysis Crystal Oscillator Circuits, Robert J. Matthys, Chapters 6, 7
Colpitts crystal oscillator phase vs gain analysis Oscillator Design and Computer Simulation, 2nd Edition, Randall W. Rhea, Chapter 11.2
Crystal drive level equations Intel application note AP-155 (Oscillators for Microcontrollers), Appendix A
Common collector gain equations Common collector, Wikipedia
Transistor biasing RF Circuit Design, Chris Bowick, Chapter 6