TELECOMMUNICATIONS Dr. Hugh Blanton ENTC 4307/ENTC 5307

Dr. Blanton - ENTC Oscillators 2 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 Oscillators 3 The basic conceptual operation of a sinusoidal oscillator can be described with the linear feedback circuit. V i (  V o ( 

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

Dr. Blanton - ENTC Oscillators 5

Dr. Blanton - ENTC Oscillators 6 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 Oscillators 7 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 Oscillators 8 All of these variations can be represented by a general oscillator circuit.

Dr. Blanton - ENTC Oscillators 9 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 G i and G o, respectively, with a transistor transconductance g m. 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 Oscillators 10 A common emitter/source configuration can be obtained by setting V 2 = 0, while common base/gate or common collector/drain configurations can be modeled by setting either V 1 = 0 or V 4 = 0, respectively.

Dr. Blanton - ENTC Oscillators 11 The feedback path is achieved by connecting node V 3 to node V 4. Writing Kirchoff’s current law for the four voltage nodes of the circuit gives the following matrix equation:

Dr. Blanton - ENTC Oscillators 12 Recall from circuit analysis that if the i th node of the circuit is grounded, so that V = 0, the matrix will be modified by eliminating the i th 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 Oscillators 13 Oscillators Using a Common Emitter BJT Consider an oscillator using a bipolar junction transistor in a common emitter configuration. V 2 = 0, with feedback provided from the collector, so that V 3 = V 4. In addition, the output admittance of the transistor is negligible, so we set G o = 0.

Dr. Blanton - ENTC Oscillators 14 These conditions serve to reduce the matrix to the following: where V = V 3 = V 4

Dr. Blanton - ENTC Oscillators 15 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 Y 1,Y 2, and Y 3 must be imaginary, so we let Y 1 = jB 1, Y 2 = jB 2. and Y 3 = jB 3. Also, recall that the transconductance, g m, and transistor input conductance are G i, are real.

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

Dr. Blanton - ENTC Oscillators 17 Since g m and G i are positive, X 1 and X 2 must have the same sign, and therefore are either both capacitors or both inductors. Since X 1 and X 2 have the same sign, X 3 must be opposite in sign from X 1 and X 2, and therefore the opposite type of component. This conclusion leads to two of the most commonly used oscillator circuits.

Dr. Blanton - ENTC Oscillators 18 Colpitts Oscillator If X 1 and X 2 are capacitors and X 3 is an inductor, we have a Colpitts oscillator.

Dr. Blanton - ENTC Oscillators 19 Hartley Oscillator If we choose X 1 and X 2 to be inductors, and X 3 to be a capacitor, we have a Hartley oscillator.

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

Dr. Blanton - ENTC Oscillators 21 Determine the frequency of the tank circuit— which sets the oscillation frequency. When we display the output waveform (from 0 to 10  s), 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 Oscillators 22 Again, display the output waveform from 0 to 10  s. This time the signal exists—but clearly, it has not reached steady-state conditions by 10  s. Using the No-Print Delay option, display the waveform from 200 to 210  s. Measure the resonant frequency and compare it to the calculated value. Are they similar?

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