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RF Oscillators

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RF Oscillators Islamic University of Gaza Communications Engineering I (Lab.) Faculty of Engineering Prepared by: Electrical Department Eng. Mohammed K. Abu Foul Experiment # (1) RF Oscillators Prelab: 1. Describe the conditions of oscillation that the Colpitts oscillator and Hartley oscillator can operate in a proper way. 2. Try to design a Hartley oscillator as shown in figure 1.9 with 5 MHz output frequency, and then find the values of C3, L1 and L2. 3. Briefly describe the advantages of crystal oscillator. 4. Briefly describe the design concepts of voltage controlled oscillators. Experiment Objectives: 1. To understand the basic theory of oscillators. 2. To design and implement the Colpitts and Hartley oscillators. 3. To design and implement the crystal and voltage controlled oscillators. 4. To understand the measurement and calculation of the output frequency of oscillator. Experiment theory: Nowadays, wireless communication is widely used in and expanded rapidly. Therefore, RF oscillators become one of the important members in wireless communications. The characteristic of oscillator is that it can produce sinusoidal wave or square wave at output terminal without any input signal. So oscillator becomes an important role no matter for modulated signals or carrier signals. In this experiment, we will focus on the theory of feedback oscillators and the design and implementation of different kinds of oscillators. Besides, we can also learn to measure and calculate the output frequency of oscillators in this experiment. 1. The operation theory of oscillators. Figure 1.1 shows the basic block diagram of the oscillator circuit. It includes an amplifier and a resonator, which comprise the positive feedback network. When we switch on the power, the circuit will produce noise. The noise will be amplified by the amplifier, and pass through a resonator circuit which has filter function. At last what's left is the signal in the passband. The unwanted signal is filtered by the resonator. So the pass through signal will then send to the input port of amplifier and combine to the original signal, which their phases are same and will amplified again. In figure 1.1, the transfer function can be expressed as: 1 The definition of open loop gain is: Using Barkhausen principle, we know the oscillation condition is: Therefore, we can obtain a specific corner frequency ωo to ensure that the open loop o gain L(jwo) is equal to 1, and the phase must be 0 , that is: Figure 1.1 Basic block diagram of oscillator circuit. From the above mentioned, in order to satisfy equations (1.3) and (1.4), we should make sure that the product of the feedback factor and the amplifier gain is 1. Meanwhile, the total summation of the phases is zero after feedback. Therefore, figure 1.1 can be changed to figure 1.2 for different structures of amplifier. Figure 1.2 Oscillator circuits comprised by non-inverting and inverting amplifier. 2 2. Colpitts and Hartley Oscillators. Figure 1.3 shows the basic structure of LC feedback oscillator which Z1, Z2 and Z3 represent inductance or capacitance components. Figure 1.4 is a small signal equivalent circuit for LC feedback oscillator. from figure 1.4, we get: Let Zi = jXi , where ZL = jXL and ZC = jXC = j(-1/ωc) , Substitute into equation 1.5, we get: From equation 1.4, we know that the Aβ is real number, therefore, the first condition for LC feedback oscillator to oscillate is: = 0 ………………………. 1.7 From equation 1.3: So, the second condition is: ……………………………………. 1.8 Figure 1.3 Feedback oscillator diagram 3 Figure 1.4 Small signal equivalent circuit for LC feedback oscillator. From the above-mentioned terms, we can make a conclusion: The basic diagram of an oscillator includes an amplifier and a resonator to form a feedback network. When we switch on the power, the circuit will produce noise. The noise will be amplified by the amplifier, and pass through a resonator circuit which has filter function. At last what's left is the signal in the passband. The unwanted signal is filtered by the resonator. So the pass through signal will then send to the input port of the amplifier and combine with the original signal, which their phases are same and be amplified again. This is how the oscillation been formed. On the other hand, base on Barkhausen oscillation principle, the first and second conditions inform us: 1. Since the voltage gain of the amplifier is real number, therefore Z1 and Z2 are same components with same reactance and Z3 is another component with different reactance. 2. The voltage gain (A) of the amplifier must be greater than the ratio of Z1 and Z2. Figure 1.5 shows three common types of oscillators, which are Colpitts, Hartley, and Clapp. If we combine the oscillators with transistor by utilizing either common gate mode, common drain mode or common source mode, then there are many types of oscillators mode for selection. Figure 1.6 is the AC equivalent circuit of Colpitts oscillator. the parallel LC resonant circuit links between the base and collector of transistor. So part of the voltage come from the voltage divider formed by C1 and C2, and feedback to the base of the transistor. R represents the total summation of output resistor, load resistor together with the equivalent resistor of the inductor and capacitor of a transistor. Figure 1.5 Three common types of oscillators. 4 Figure 1.6 AC equivalent circuit of Colpitts oscillator. If the operation frequency is low, then we can ignore the internal junction capacitance of the transistor. Hence, from equation 1.7, the oscillation frequency of Colpitts oscillator is: We need to consider the conditions of Colpitts oscillator. the voltage gain of (A) of the amplifier is gmR. then, from equation 1.8, we know that condition of oscillation is: Figure 1.7 is the circuit diagram of Colpitts oscillator. R1, R2, and R3 provide operation bias to transistor, C1 is coupling capacitor, C2 is bypass capacitor, C3, C4 and L1 comprise a resonant circuit for selecting suitable operation frequency. Figure 1.7 Circuit diagram of Colpitts oscillator. 5 Figure 1.8 AC equivalent circuit of Hartley oscillator Figure 1.8 is the AC equivalent circuit of Hartley oscillator. Same as Colpitts oscillator, the parallel LC resonant circuit connects between the base and collector of the transistor, the difference is part of the voltage come from the voltage divider formed by L1 and L2 and feedback to the base of the transistor. (R) represents the total summation of output resistor, load resistor together with the equivalent resistor of the inductor and capacitor of a transistor. If the operation frequency is low, then we can ignore the internal junction capacitance of the transistor. Hence, from equation 1.7, the oscillation frequency can be obtained as: Similarly, from equation 1.8, we can obtain the condition of oscillation as: Figure 1.9 is the circuit diagram of Hartley oscillator. R1, R2 and R3 provide the operation bias to transistor, C1 is coupling capacitor, C2 is bypass capacitor, C3, L1 and L2 comprise a resonant circuit for selecting suitable operation frequency. Figure 1.9 Circuit diagram of Hartley oscillator. 6 3. Crystal Oscillator. In order to get better frequency stability, it is obvious that we have to choose a high Q circuit when designing the oscillator circuits, such as transistors with piezoelectric effect, for example, quartz, ceramic and so on. These transistors are usually used to design the oscillator circuits with high stability due to the reason that the loss of the transistors is very low and the Q value of the transistors is very high and stable. Crystals are tri-dimensional structure. It is a mechanical oscillator, which has various types of oscillation. A crystal is a device that is usually made by cutting a pure quartz crystal in a very thin slice and then plating the faces with a conductor in order to make an electrical connection. The property that makes the crystal useful in designing the oscillator is the piezoelectric effect. When the crystal is excited by the voltage, it will cause a deformation of the quartz material and produce various types of oscillation. In addition, we can choose specific oscillation type and high order harmonic via different product process of crystals. Figure 1.10 shows the equivalent circuit and the impedance characteristic of crystal. In figure 1.10a, the parallel capacitor Cp is the static capacitor in the range about 7 to 10 pF. The series capacitor Cs and inductor L correspond to the disposal sequence and mass of crystal. Generally, the value of Cs is about 0.05 pF, and (L) is about 10 H. the internal loss is represented by resistor (r), which mainly comes from plating, brace of the crystal and the impedance caused by inner-friction or leads etc. Since the Q value of crystal is very high, therefore, (r) seems to be very small, only few ohms. Besides, we also can get the series or parallel resonant frequency, respectively. In figure 1.10, we have: Figure 1.10 Equivalent circuit of crystal and the characteristic curve of impedance. Since Cp ≈ 140 Cs, then the difference between fs and fp is around 0.36%. 7 Crystal always plays a role as the parallel or series resonant circuit in oscillator circuit. Due to the high Q value of crystals, the stability of oscillation frequency can be higher than using the general inductors and capacitors. If crystal is used in a parallel resonant circuit, then it is called as the parallel mode crystal oscillator, as shown in figure 1.11a. In the oscillation circuit with parallel mode, the crystal can be seen as an inductor.
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