1. Microwave Oscillator By Professor Syed Idris Syed Hassan
Sch of Elect. & Electron Eng
Engineering Campus USM
Nibong Tebal 14300
SPS Penang

2. One-port negative Oscillator using IMPATT or Gunn diodes
Negative resistance device is usually a biased diode. Oscillation
occurred whence ZL= -Zinwhich implies

3. Stability of oscillation
Oscillation takes place when the circuit first unstable, i.e Rin +RL < 0 .
Rin depends on current and frequency. Any transient or noise will excite or cause oscillation . The oscillation will become stable when Rin +RL=0 and Xin +XL=0. The stable frequency is fo.
Let’s ZT(I,s)= Zin(I,s) +ZL(s)
Where I current and s=jw is a complex frequency. Then for a small change in current dI and in frequency ds, the Taylor’s series for ZT(I,s) is

4. Continue (stability) Or subst ZT=RT+jXT Use the fact that
Where ds=da+jdw
Therefore
If the transient caused by dI and ds to decay we must have da < 0 when dI>0 so that
Or subst ZT=RT+jXT

5. Continue ( stability)
For passive load
By substituting ZT=Zin + ZL, the stability equation reduces to
Where Zin = Rin + j Xin
ZL =RL + jXL

6. Matching diode oscillator
Eg. A negative -resistive diode having Gin=1.25 /40o (Zo=50ohm) at its desired operating point , for 6 GHz . Design a load matching network for one-port of 50 ohm load oscillator.
By plotting ZL in Smith chart then match to 50 ohm as usual. The
50W

7. FET oscillator
Choose high degree of unstable device. Typically, common
source or common gate are used.Often positive feedback to
enhance instability.
Draw output stable circle and choose GT for large negative
resistance (I.e Zin). Then take ZL to match Zin. Choose RL such that RL+Rin < 0, otherwise oscillation will cease.

8. Design Usually we have to choose For resonation And For steady -state
where
We can proved that

9. FET common gate
Design 4GHz oscillator using common gate FET configuration
with 5nH inductor to increase instability. Output port is 50W. S-
parameter for FET with common source configuration are : (Zo=50W) S11= 0.72/-116o, S21=2.6/76o, S12=0.03/57o,S22=0.73/-54o.
5nH

10. continue First we have to convert from common source S-parameter
to common gate with series inductor S-parameter. This is
usually done using CAD. The new S-parameter is given by
S11’= 2.18/-35o, S21’=2.75/96o, S12’=1.26/18o,S22’=0.52/155o.
Thus the output stability circle parameters are given as
where

11. To determine GT
Since S’11>1, thus the stable region is inside the shaded circle.
GT can be choose anywhere in the Smith chart but the main objective Gin should be larger than 1. Let say we choose GT=0.59/-104. Then calculate Gin, thus
Or Zin= j1.9 W
Then

12. Using a transmission line to match a resistive load, thus we have a length of l and a load of 89.5 W. Using Rin/3 should ensure enough instability for the startup of oscillator. It is easier to implement ZL =90 ohm . The steady -state oscillation frequency will differ from 4Ghz due to the nonlinearity of the transistor
0.346l
For GT matching, we can use open-stub to match 50 ohm. Plot GT and then determine the YT. Moving towards load until meet the crossing point between SWR circle and the unity circle. That the distant between transistor and the stub. Obtain the susceptance and distance towards open circuit.
Towards generator GL
0.319l GT

13. Dielectric resonator Equivalent series impedance
Where N =coupling factor/turn ratio
Q=R/woL (unloaded resonator)
Ratio of unloaded to external Q is given by
where
RL=2Zo for loaded resistance
= Zo for l/4 transmission line

14. Continue (Dielectric resonator)
Reflection coefficient looking on terminated microstrip feedline towards resonator is given by or
Q can be determined by simple measurement of reflection coefficient

15. Dielectric resonator oscillator
Series feedback
Parallel feedback

16. Example (dielectric resonator osc.)
Design 2.4GHz dielectric resonator oscillator using series feedback with bipolar transistor having S-parameters (Zo=50ohm); S11= 1.8 / 130o , S12= 0.4 / 45o , S21= 3.8 /36o, S22= 0.7 / -63o. Determine the required coupling coefficient for dielectric resonator and matching.
Solution
Circuit layout

17. continue Procedures Plot the stability circles 2. Choose a point Gin
Inside the instability area

18. continue Calculate the Gout and Gin = GL using this formula
We obtain Gout = 10.7/132o. This corresponding to
Then

19. Continue (output matching)X
So we have
d1=0.034l l1=0.193 l
Or d1=0.429l l1=0.307l

20. Network at resonator
Resonator should be placed at zero or 180o of phase from the transistor. So we have either l (zero phase) or l (180o phase)
d2= l
Or = l

21. Noise in oscillator Amplitude noise Phase noise Flicker noise
Phase noise-may be due to variation of device capacitance with variation of voltage.This is usually happened in amplifier.Amplitude noise may be converted to phase noise if the amplifier is present. Noises cause frequency instability in oscillator.

22. Noise to Carrier Ratio (NCR)
Parallel impedances for Rp , Lp , and Cp can be written as
where
and

23. NCR Limit (cont) The transfer function of the oscillator is given by
Then substitute for Zp , we have

24. NCR (cont) At oscillation
Where fo=oscillation frequency
And the gain condition (Barkhausen) for oscillation is gmRp=1
Thus, any changes will result #%

25. NCR (cont)
In the oscillator model, the noise source is Rp .The noise current produced is
where
k=Boltzman const , T = absolute temp.
B= bandwidth
Since gm= 1/Rp and Iout= gm * Vin , the noise current can be transferred to input and hence Vin can be written as
**%%

26. NCR (cont)
Thus the Vout, can be obtained by substituting and squaring #% and **%% . We have
Taking B= 1 Hz and carrier voltage ,Vcarrier-rms
And the carrier power is given by
The noise to carrier ratio for SSB in Hz is given by
Where fm =offset frequency from carrier

27. NCR (cont) For phase noise
Note: This ratio is half of the total noise since half will be converted to AM noise and half left for phase noise.

28. Example
Calculate the phase noise to carrier ratio of an oscillator of 10MHz with Q=100. Assume the inductor is 2 mH and the peak voltage across it is 10V. Let the noise figure is 10dB.

29. Flicker noise ( 1/f noise)
As in previous example
fm NCR
50kHz 170dB/Hz
30kHz dB/Hz
10kHz 159dB/Hz

30. Design for low 1/f noise (FET) (HBT) Maximum oscillation frequency
Design procedures:-
Choose high Q-factor of the resonator
Choose low 1/f noise active components (e.g Bipolar transistor)
Choose transistor with the lowest possibility of fT . For good rule of thumb fT < 2 x fosz .
Low current best 1/f performance. Note that fT drops with low current.
(FET)
(HBT)
Maximum oscillation frequency
(BJT)
For high Q-factor choose parts that have low losses:
Resonator
Series resistance of capacitors
Series resistance of tuning diode
PCB.

31. Measure phase noise from VNA (for checking)
Verify power input signal no higher than 10dBm
Reduce input attenuation to minimum (0 dB)
Determine the carrier power at large video and resolution bandwidth at appropriate span (3MHz RBW, 1MHz VBW,50MHz span.
Set span for single sideband ( desired offset frequency)
Reduce VBW to 10 Hz, RBW to 1 kHz.
Set marker to the carrier. Select marker to show the frequency offset.
Move the marker along the SSB phase noise curve and take reading. MAX HOLD for maximum phase noise power( let the spectrum settle for 5 minutes )
Note that cable insertion loss should also be determined

32. Measure phase noise from VCO

33. Reducing Phase Noise in Oscillators
1. Maximize the Qu of the resonator.
2. Maximize reactive energy by means of a high RF voltage across the resonator. Use a low LC ratio.
3. Avoid device saturation and try to use anti parallel (back to back) tuning diodes.
4. Choose your active device with the lowest NF (noise figure).
5. Choose a device with low flicker noise, this can be reduced by RF feedback. A bipolar transistor with an unby-passed emitter resistor of 10 to 30 ohms can improve flicker noise by as much as 40 dB. - see emitter degeneration
6. The output circuits should

34. YIG oscillator
Condition for oscillation
S11’>1 and S22’>1

35. YIG equivalent circuit
fo=resonance frequency=nHo
where
V= volume of YIG sphere
k=1/d1=coupling factor and d1 is the loop diameter
wm= 2pfm=2pn (4p Ms)
Ho= dc magnetic filed
n= gyro magnetic ratio ( 28 GHz/Tesla)
DH= resonance line width
L1= self inductance of the loop
4pMs= saturation magnetism

36. Hartley Oscillator

37. Colpitts Oscillator

38. Effects of ambient changes on stability in oscillators
A frequency change of a few tens of hertz back and forth over a couple of minutes would mean nothing to an entertainment receiver designed for the FM Radio band. Such a drift in an otherwise contest grade receiver designed to receive CW (morse code) would be intolerable. It's a question of relativity.