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AE_Lecture11_Part2_Radio-Frequency Oscillators

Module by: Bijay_Kumar Sharma. E-mail the author

Summary: AE_Lecture11_Part2 describes the Radio-Frequency Oscillators.

AE_LECTURE 11_Part2.

Part 2 deals with RF Oscillators.

Section 1. Class of RF OSCILLATORS

(100kHz- 1000kHz:Medium Wave RF & 1MHz-30MHz:Short Wave RF;

30MHz-70MHz: Amateur Band for HAM Radio practitioners;

70MHz-300MHz: Very High Frequency (VHF) Band for FM and TV transmissions;

300MHz-800MHz: Ultra High Frequency(UHF) Band for Police Communication;

1GHz-100GHz: Microwaves for satellite communication;

Terra Hz(0.4µm-100µm): Optical Fiber Communication)

LC oscillators are RF oscillators.

Figure 1
Figure 1 (graphics1.png)

Figure 1. Parallel Resonance Circuit or Tank Circuit.

Figure 2
Figure 2 (graphics2.png)

Figure 2. Circuit Diagram of a Tank Circuit driven by a constant current source.

Parallel resonance circuit is known as tank Circuit.

Resonance frequency=ωo=

Figure 3
Figure 3 (graphics3.png)

Figure 4
Figure 4 (graphics4.png)
Figure 5
Figure 5 (graphics5.png)

Figure 6
Figure 6 (graphics6.png)

Figure 3. Magnitude of the reactance of a tank circuit vs frequency.

Figure 7
Figure 7 (graphics7.png)

At ω=

Figure 8
Figure 8 (graphics8.png)
;
Figure 9
Figure 9 (graphics9.png)

Figure 10
Figure 10 (graphics10.png)
Figure 11
Figure 11 (graphics11.png)
Figure 12
Figure 12 (graphics12.png)
Figure 13
Figure 13 (graphics13.png)

When quality factor Q of the tank circuit =∞, the circuit is purely reactive and there is no dissipation.

When quality factor Q is finite say 1000 then an equivalent RP comes in parallel with the tank circuit. RP accounts for the losses

Figure 14
Figure 14 (graphics14.png)

For a finite quality factor tank circuit, the effective impedance is a pure resistance RP at resonance frequency.

Hence

Figure 15
Figure 15 (graphics15.png)

Frequency response of the tank circuit is :

Figure 16
Figure 16 (graphics16.png)

Figure 17
Figure 17 (graphics17.png)

Figure4. The peak response of a tank circuit for various quality factors.

Figure 18
Figure 18 (graphics18.png)
Figure 19
Figure 19 (graphics19.png)

At Q=∞, spike response.

At Q=finite, peak response.

As Q falls, sharpness of the peak response is lost.

Section 1.1. GENERALIZED LC OSCILLATOR.

Figure 20
Figure 20 (graphics20.png)

Figure 5. Block Diagram of generalized LC Oscillator

Figure 21
Figure 21 (graphics21.png)

Figure 22
Figure 22 (graphics22.png)

Figure 23
Figure 23 (graphics23.png)

Where

Figure 24
Figure 24 (graphics24.png)

Therefore:

Figure 25
Figure 25 (graphics25.png)

Examining the feedback network in Figure 8:

Feed back voltage

Figure 26
Figure 26 (graphics26.png)

If loop gain=1∟0˚

Figure 27
Figure 27 (graphics27.png)
Figure 28
Figure 28 (graphics28.png)
Figure 29
Figure 29 (graphics29.png)
Figure 30
Figure 30 (graphics30.png)

Figure 31
Figure 31 (graphics31.png)

This identity can be true only if

Figure 32
Figure 32 (graphics32.png)
Figure 33
Figure 33 (graphics33.png)

Subs(4) & (5) in (3)

Figure 34
Figure 34 (graphics34.png)
Figure 35
Figure 35 (graphics35.png)

Starting condition is

Figure 36
Figure 36 (graphics36.png)

This means

Figure 37
Figure 37 (graphics37.png)
are same kind of reactance and
Figure 38
Figure 38 (graphics38.png)
is of opposite kind of reactance.

Table 1. Different possible configurations of a generalized LC Oscillator.

Table 1
  Z 1 Z 2 Z 3 Type of Oscillator
1 L L C Hartley Oscillator
2 C C L Colpitts Oscillator

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