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TELECOMMUNICATIONS Dr. Hugh Blanton ENTC 4307/ENTC 5307

RADIO FREQUENCY OSCILLATORS • In the most general sense, an oscillator is a non –linear circuit that converts DC power to an AC waveform. • Most oscillators used in wireless systems provide sinusoidal outputs, thereby minimizing undesired harmonics and noise sidebands. Dr. Blanton - ENTC 4307 - Oscillators 2

The basic conceptual operation of a sinusoidal oscillator can be described with the linear feedback circuit. Vo(w) Vi (w) Dr. Blanton - ENTC 4307 - Oscillators 3

An amplifier with voltage gain A has an output voltage Vo. • This voltage passes through a feedback network with a frequency dependent transfer function H(w) and is added to the input Viof the circuit. • Thus the output voltage can be expressed as Dr. Blanton - ENTC 4307 - Oscillators 4

Dr. Blanton - ENTC 4307 - Oscillators 5

If the denominator of the previous equation becomes zero at a particular frequency, it is possible to achieve a nonzero output voltage for a zero input voltage, thus forming an oscillator. • This is known as the Barkhausen criterion. • In contrast to the design of an amplifier, where we design to achieve maximum stability, oscillator design depends on an unstable circuit. Dr. Blanton - ENTC 4307 - Oscillators 6

General Analysis • There are a large number of possible RF oscillator circuits using bipolar or field-effect transistors in either common emitter/source, base/gate, or collector/drain configurations. • Various types of feedback networks lead to the well-known oscillator circuits: • Hartley, • Colpitts, • Clapp, and • Pierce Dr. Blanton - ENTC 4307 - Oscillators 7

All of these variations can be represented by a general oscillator circuit. Dr. Blanton - ENTC 4307 - Oscillators 8

The equivalent circuit on the right-hand side of the figure is used to model either a bipolar or a field-effect transistor. • We can simplify the analysis by assuming real input and output admittances of the transistor, defined as Gi and Go, respectively, with a transistor transconductance gm. • The feedback network on the left side of the circuit is formed from three admittances in a bridged-T configuration. • These components are usually reactive elements (capacitors or inductors) in order to provide a frequency selective transfer function with high Q. Dr. Blanton - ENTC 4307 - Oscillators 9

A common emitter/source configuration can be obtained by setting V2 = 0, while common base/gate or common collector/drain configurations can be modeled by setting either V1 = 0 or V4 = 0, respectively. Dr. Blanton - ENTC 4307 - Oscillators 10

The feedback path is achieved by connecting node V3to node V4. • Writing Kirchoff’s current law for the four voltage nodes of the circuit gives the following matrix equation: Dr. Blanton - ENTC 4307 - Oscillators 11

Recall from circuit analysis that if the ith node of the circuit is grounded, so that V = 0, the matrix will be modified by eliminating the ith row and column, reducing the order of the matrix by one. • Additionally, if two nodes are connected together, the matrix is modified by adding the corresponding rows and columns. Dr. Blanton - ENTC 4307 - Oscillators 12

Oscillators Using a Common Emitter BJT • Consider an oscillator using a bipolar junction transistor in a common emitter configuration. • V2= 0, with feedback provided from the collector, so that V3= V4. • In addition, the output admittance of the transistor is negligible, so we set Go = 0. Dr. Blanton - ENTC 4307 - Oscillators 13

These conditions serve to reduce the matrix to the following: • where V = V3= V4 Dr. Blanton - ENTC 4307 - Oscillators 14

If the circuit is to operate as an oscillator, then the new determinant must be satisfied for nonzero values of V1 and V, so the determinant of the matrix must be zero. • If the feedback network consists only of lossless capacitors and inductors, then Y1,Y2, and Y3must be imaginary, so we let Y1= jB1, Y2= jB2. and Y3 = jB3. • Also, recall that the transconductance, gm , and transistor input conductance are Gi, are real. Dr. Blanton - ENTC 4307 - Oscillators 15

Then the determinant simplifies to Dr. Blanton - ENTC 4307 - Oscillators 16

Since gm and Gi are positive, X1 and X2 must have the same sign, and therefore are either both capacitors or both inductors. • Since X1 and X2 have the same sign, X3 must be opposite in sign from X1 and X2, and therefore the opposite type of component. • This conclusion leads to two of the most commonly used oscillator circuits. Dr. Blanton - ENTC 4307 - Oscillators 17

Colpitts Oscillator • If X1 and X2 are capacitors and X3 is an inductor, we have a Colpitts oscillator. Dr. Blanton - ENTC 4307 - Oscillators 18

Hartley Oscillator • If we choose X1 and X2 to be inductors, and X3 to be a capacitor, we have a Hartley oscillator. Dr. Blanton - ENTC 4307 - Oscillators 19

Lab 5 • Implement the following Colpitts oscillator using PSpice. Dr. Blanton - ENTC 4307 - Oscillators 20

Determine the frequency of the tank circuit—which sets the oscillation frequency. • When we display the output waveform (from 0 to 10 ms), there is no signal! • The problem is one of insufficient spark. • One solution is to pre-charge one of the tank capacitors. • Using either CT1 or CT2, initialize either capacitor with a small voltage (such as .1 v). Dr. Blanton - ENTC 4307 - Oscillators 21

Again, display the output waveform from 0 to 10 ms. • This time the signal exists—but clearly, ithas not reached steady-state conditions by 10 ms. • Using the No-Print Delay option, display the waveform from 200 to 210 ms. • Measure the resonant frequency and compare it to the calculated value. • Are they similar? Dr. Blanton - ENTC 4307 - Oscillators 22

Add a plot of Vf (the feedback signal shown in the figure). • Is Vf 180 out of phase with Vout? • Generate a frequency spectrum for the Colpitts oscillator. • Is there a DC component? • Does the fundamental frequency approximately equal measured the time-domain frequency? Dr. Blanton - ENTC 4307 - Oscillators 23

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