The SFG of a third-order oscillator
is shown in Fig.1.á. The implementation of this SFG
could be done by using the topology in Fig.1.â. This is a feedback loop that consists of a current amplifier-inverter
(180^{o} phase shift), and a third-order lowpass LC network for
introducing an additional phase shift of 180^{o} in order the total
phase shift in the loop to be equal to zero.

**Fig.1 ****á****) SFG of a third-order oscillator**

** ****â****) Implementation of the SFG in Fig.1a**

** **

** **

The loop gain of the circuit in Fig.1.â is given by

_{}_{}

According to the above expression,
we can calculate the phase of the loop as,

_{}_{}

_{ }

The
phase become equal to zero at a specific frequency *ù _{o}*

_{}_{}

which is the oscillation frequency.

The loop gain will be become equal
to one if the following condition is fulfilled

_{}_{}

_{ }

This relationship
describes the condition of oscillation.

In the
topology of Fig.1â capacitors can be replaced by
inductors and the inductor can be replaced by a capacitor to create a highpass
third order LC network. This topology is the well-known **Hartley **oscillator.

A real circuit of a Colpitts oscillator,
using a BJT as an active element, is shown in Fig.2; note that in this case ** A**=

** **

**Fig.2 ****á****) Colpitts oscillator realized using
a BJT transistor**

**â****) Small-signal eqivalent of the circuit in Fig.2a**

Colpitts oscillators are suitable for operation at radio frequencies.

** **

Using a BJT with h_{fe}=100, we will design a
Colpitts oscillator at f_{o} =2 MHz.

According to the condition of oscillation

_{}_{}

or,

_{}_{}

The frequency of oscillation is defined by,

_{}

_{}

or,

_{}

_{
}

Choosing,

_{}_{}

_{ }

and *C*_{2}=3.2 *nF* it results, *C*_{1}=320
*nF * and L=1,97 *ì**H*.