# 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!

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:

$$\mathbf{f}_{c} = \frac{1}{2 \pi RC}\\$$

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!

# Colpitts Crystal Oscillator Design

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

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

# Jim Williams’ Analog IQ #14

This week’s analog IQ test leads us down the road of BJT temperature sensors, delta Vbe’s, and diode theory! But how well does the theory hold up in the real world?

Description Reference
PN junction temperature curves The Effect of Temperature on Diode Characteristics, Concepts Electronics
Accurate Temperature Sensing with an External P-N Junction Linear Technologies Application Note 137, Michael Jones
The Brokaw band-gap circuit, explained by Paul Brokaw himself! A Transistor Voltage Reference and What the Band-Gap Has To Do With it, A. Paul Brokaw
Measured temperature vs Vbe characteristics What’s All This VBE Stuff, Anyhow?, Bob Pease

# Fixing the MHS-5200A

Today we make some simple and cheap modifications in order to address the two biggest problems in the MHS5200A function generator: sine wave harmonic distortion, and square wave ringing/overshoot.

If you want to make the same modifications, here is the Digikey BOM. Note that the capacitors and inductors I used for the Bessel filter were 0402, while the pads on the PCB are 0603; either size fits, though 0402’s are obviously a bit harder to work with.

See the pictures below for more details.

Board Overview

Replacing the AD812 With the THS3092 (Be Sure to Replace the Heatsink!)

Modifying the DAC Filter(s)

Bessel Filter Components