# Simple MF Colpitts Oscillator

### Reference Circuit

The following Colpitts Oscillator is built around a 2N3904 transistor.  I verified its operation for various frequencies from 250 kHz to 1.5 MHz.  The inductor is 20 turns of insulated 22 AWG wire on a 1.5 inch diameter cardboard core (the turns are as closely wound as practical, taking about 1.0 inches axially along the core).  I measure the inductance as approximately $L \approx 11 \mu H$.  Capacitor values for the LC tank (lower left of schematic) are presented in a table.

Capacitor Value Observed Frequency
$1.5\, nF$ $1.6\, MHz$
$10\, nF$ $670\, kHz$
$33\, nF$ $370\, kHz$
$68\, nF$ $250\, kHz$

The oscillator gave best performance at capacitor values 33 nF and 22 nF.

# Measuring Inductance

### Problem

Measuring inductance is a complex task.  Methods proposed elsewhere require precise measurements with an oscilloscope in its usual (voltage vs. time) display mode.  Methods based on building a filter with the inductor and finding the cutoff or natural frequency assume a sufficiently high-Q that peak/null detection is obvious.  In practice, I find these methods hard to apply.

Is there an easier method to measure inductance using a hobby-grade oscilloscope?

# AC Coupling using an Emitter Follower

Problem

Input signals often have a DC component that is not of interest and inconvenient to work with.  The DC component might be unknown or of a value that doesn’t match the circuit the input is driving.  Under standard linear circuit  assumptions, the response to the time-varying component of the input is independent of the DC component, so we can strip away the DC component and replace it with a more convenient value.  A blocking capacitor generally provides the “AC Coupling” of the input signal.

A problem with blocking capacitors arises when I try to select one for my audio circuits.  To the signal source, my circuit appears to have some input impedance, R, and the equivalent circuit becomes a single-pole high-pass filter:

The commonly-defined “cut-off” frequency for such a circuit is $f_{c}=\frac{1}{2\pi RC}$, and I often try to have a cut-off frequency one decade below my lowest frequency of interest.  To accomplish this I need a very large RC product, but the input impedance of my circuit is generally too low. Continue reading AC Coupling using an Emitter Follower