experiment # (1) rf oscillators -...

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Islamic University of Gaza

Faculty of Engineering

Electrical Department

Communications Engineering I (Lab.)

Prepared by:

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:

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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

gain L(jwo) is equal to 1, and the phase must be 0o, 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.

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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

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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.

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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.

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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.

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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%.

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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. On the other hand, if the

crystal is operated in series resonant circuit, then it is called as the series mode crystal

oscillators as shown in figure 1.11b. In the oscillation circuit with series mode, the crystal can

be seen as a capacitor.

Besides, the design of crystal oscillator is similar to the design methods without using

crystals. However, we should pay more attention to design the bias circuit for the reason that

the DC signal may not pass through the crystal.

Figure 1.11 Circuit structures of crystal oscillator.

Figure 1.12 Circuit diagram of the Colpitts crystal oscillator.

Figure 1.12 is the circuit diagram of the Colpitts crystal oscillator. The operating bias of

the transistor is provided by R1, R2, and R3. Moreover, C1 and C2 are the external parallel

capacitors added on the crystal. The values that we choose should be higher until the parasitic

capacitor can be neglected. The bypass capacitor and coupled capacitor are denoted as C3 and

C4, respectively. The oscillation frequency of this circuit is decided by the frequency of the

crystal oscillator we used.

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4. Voltage Controlled Oscillator (VCO).

Voltage controlled oscillator is an oscillator circuit that the output frequency can be

varied by voltage. The main design concepts and methods are similar to the LC feedback

oscillator as mentioned before. However, the only difference is that we use varactor diode,

which the capacitance can be varied by the voltage to replace the original capacitor. Therefore,

we may not discuss the theory of oscillator but we will focus on the theory of the varactor

diode.

Varactor diode or tuning diode is mainly used for changing the capacitance value of

oscillator. the objective is to let the output frequency of oscillator can be adjusted or tunable,

therefore varactor diode dominates the tunable range of the whole voltage controlled oscillator.

Varactor diode is a diode, which its capacitance can be varied by adding a reverse bias voltage

to pn junction. When reverse bias voltage increases, the depletion region become wide, this will

cause the capacitance value decreases; nevertheless when reverse bias voltage decreases, the

depletion region will be reduced, this will cause the capacitance value increases. Varactor diode

also can be varied from the amplitude of AC signal.

Figure 1.13 is the capacitance analog diagram of varactor diode. When a varactor diode

without bias voltage, the concentration will be differed from minor carriers at pn junction. Then

these carriers will diffuse and become depletion region. The p type depletion region carries

electron positive ions, then the n type depletion region carries negative ions. We can use

parallel plate capacitor to obtain the expression as shown as follow:

………………….. 1.16

Where:

ᵋ = 11.8 ᵋo (dielectric constant of silicon)

ᵋo = 8.85 × 10-12

A: the cross section area of capacitor.

d: the width of depletion region.

When reverse bias voltage increases, the width of depletion region d will increase but

the cross section area A remains, therefore the capacitance value would be reduced. On the

other hand, the capacitance value will increase when reverse bias voltage decreases.

Varactor diode can be equivalent to a capacitor series a resistor (Rs) and an inductor (Ls)

as shown in figure 1.14. From figure 1.14, Cj is the junction capacitor of semiconductor, which

only exits in pn junction. Rs is the sum of bulk resistance and contact resistance of

semiconductor material which is related to the quality of varactor diode (generally below a few

ohm). Ls is the equivalent inductor of bounding wire and semiconductor material.

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Figure 1.20 is the circuit diagram of voltage controlled oscillator by using the structure

of Clapp oscillator in figure 1.10c. R1, R2, and R3 provide the operating bias voltage of the

transistor. C2, C3, L1, CV1 and CV2 comprise the resonant circuit to select a proper operation

frequency. Finally, C1 is the bypass capacitor and C4 is the coupled capacitor.

Figure 1.13 Capacitance analog diagram of varactor diode.

Figure 1.14 Circuit symbol and equivalent circuit diagram of varactor diode.

Figure 1.15 Circuit diagram of voltage controlled oscillator

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Experiment items:

Experiment 1: Colpitts and Hartley oscillators

1. To implement the circuit as shown in figure 1.7 which L1=27µH, C3=1nF, C4=15nF or

refer to figure ACS2-1 on ETEK ACS-3000-01 module. Let J1 and J2 be short circuit,

J3 and J4 be open circuit.

2. Switch the oscilloscope, then observe on the output signal port (O/P) and the feedback

port (TP1) of the oscillator. Then record the signal waveforms and frequencies in table

1.1.

3. To implement the circuit as shown in figure 1.9 which L2=220µH, L3=100µH, C5=10nF

or refer to figure ACS2-1 on ETEK ACS-3000-01 module. Let J3 and J4 be short

circuit, J1 and J2 be open circuit.



1.1.

Experiment 2: Crystal and voltage controlled oscillator

1. To implement the circuit as shown in figure 1.12 which C2 = C3=680pF, X'tal=6MHz or

refer to figure ACS2-2 on ETEK ACS-3000-01 module. Let J2 be short circuit, J1 be

open circuit.



1.2.

3. To implement the circuit as shown in figure 1.15 which C2 = C3=680pF, L1=100µH,

CV1=CV2=1SV55 or refer to figure ACS2-2 on ETEK ACS-3000-01 module. Let J1 be

short circuit, J2 be open circuit.

4. Adjust the variable resistor VR1, so that the DC voltage (Vt) of the varactor diode is

varied from the values in table 1.3.

5. Switch the oscilloscope, then observe on the output signal port (O/P) and record the

measured results in table 1.3.

6. According to the data in table 1.3, sketch the characteristic curve with frequency versus

voltage in figure 1.16

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Measured results:

Table 1-1 measured results of Colpitts and Hartley oscillator

Components values of

Colpitts oscillator Output signal waveforms

L1= ……….

C3= ………..

C4= ………..

O/P

TP1

Theoretical value fo = ……………………..

Measured value fo = ………………………

Components values of

Hartley oscillator Output signal waveforms

L2= ……….

L3= ………..

C5= ………..

O/P

TP1



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Table 1-2 Measured results of crystal oscillator

Output signal waveforms Components values

C2= ……………., C3= ………….., X'tal= ……………….

O/P



TP1



Table 1-3 Measured results of voltage controlled oscillator

Input DC bias

(Vt) 3 4 5 6 7 8 9 10 11 12

Output signal

frequency

(MHz)

Figure 1.16 Characteristic curve of frequency versus voltage

3 4 5 6 7 8 9 10 11 12

Input DC

bias (Vt)

Output signal

frequency (MHz)

experiment # (1) rf oscillators -...

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