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Module by: Bijay_Kumar Sharma. E-mail the author

Summary: AE_Lecture11_Part3 deals with the specefic RF Oscillators such as Colpitts, Hartley, Tuned and Crystal Oscillator.

Section 1.2. Colpitts Oscillator Using Op-Amp

Theoretical Analytical results have been taken from”Microelectronic Circuits_Analysis & Design” by Rashid, Publisher Thomson(Indian Edition),1999.Chapter 14_Power Amplifiers.

Figure 8. Circuit Diagram of Colpitts Oscillator.

The frequency of oscillation:

The Barkhausen Criteria is satisfied by the following ratio:

gmR1=C2/C1+(C1/C2)(R1/RL)+(L/(C2RL^2))+L/(C1R1RL)

For large values of RL: gmR1=C2/C1 and gm=Aopen/RL

But magnitude of Aopen = magnitude of the voltage gain of the Basic Amplifier in Figure 8. The basic amplifier is an inverting amplifier hence /Aopen/= RF/R1

Therefore gmR1=(Aopen/RL)R1=(RF/R1)*(R1/RL)=RF/RL=C2/C1;

Therefore when RL is large then we must satisfy the condition:RF/RL = C2/C1

A typical Colpitts oscillator with fosc at 150kHz will have the component values as follows:

R1 = 100kohm, RF= 1000kohm, RL = 100kohm,C1=0.01uF,C2=0.1uF,L=124uH

Section 1.2.1.Colpitt’s oscillator Using BJT

Figure 9.Circuit Diagram of Colpitts Oscillator using BJT.

Section 1.3.1. Hartley Oscillator Using Op-Amp

Figure 10. Circuit Diagram of Hartley Oscillator using Op.Amp.

For oscillation:

gmR1 = (L1/L2)+(R1.L2)/(RL.L1)

For large values of RL,

gm.R1 = L1/L2

But gm = Aopen/RL and /Aopen/ = RF/R1

Therefore gmR1=RF/RL =(L1/L2)+(R1.L2)/(RL.L1)

Typical device parameters of a Hartley Oscillator with fosc = 33kHz are:

R1=100kohms, RF = 1Mohms, RL = 900kohms, L1=L2=125uH, C = 0.1uF.

Section 1.3.2. HARTLEY OSCILLATOR USING JFET

Figure 11. Circuit Diagram of Hartley Oscillator using JFET.

Here

Section 1.4. TUNED OSCILLATOR

Figure 12. Circuit diagram of a tuned oscillator.

Section 2. CRYSTAL OSCILLATOR

In Colpitts oscillator, inductor is replaced by a crystal.

Quartz crystal is preferred due to the stability and accuracy.

Figure 13. The symbol of a quartz crystal, the equivalent circuit, pole-zero pattern of a crystal resonance circuit.

Q(of series resistance)=

Q(Of Tank Circuit)=

Mass of the crystal gives rise to Ls

Elasticity of the crystals gives rise to Cs.

Damping force gives rise to Rs.

LS, CS and RS comprises the intrinsic series resonance path through the crystal.

Table 2. COMMON CUTS OF QUARTZ CRYSTAL(RCA Corp.)

 Frequency 32kHz 280kHz 525kHz 2MHz 10MHz Cut XY Bar DT DT AT AT Rs 40KΩ 1820Ω 1400Ω 82Ω 5Ω L 4800H 25.9H 12.7H 0.52H 12mH Cs(pF) 0.0491 0.0126 0.00724 0.0122 0.0145 Cp(pF) 2.85 5.62 3.44 4.27 4.35 Q 25,000 25,000 30,000 80,000 150,000

Section 2.1.CRYSTAL OSCILLATOR CIRCUIT

Figure 14. Crystal Oscillator circuit using an Op.Amp.

The tank circuit of CRYSTAL OSCILLATOR

EXACT RELATION

When Q is very high which is true for crystal then Re~0.

And

In near future, we will have a Paradigm Shift. The scaling of CMOS will hit the wall. For that day we are developing ‘ MICROELECTROMECHANICAL SYSTEM(M E M S)’,Molecular Electronics & Nanotechnology.

We have to replace low Q integrated capacitor & inductors. These will be replaced by MEMS structure. MEMS & CMOS will enable highly efficient single chip radio.

In 2002 Hewlett-Packard & HCLA announced a molecular array with 100nm center to center memory element spacing(9/10/02)

If we achieve 35nm center to center we will achieve 100 Gb memory space in 1(cm)2.

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