Microwave Oscillator. By Professor Syed Idris Syed Hassan Sch of Elect. & Electron Eng Engineering Campus USM Nibong Tebal 14300 SPS Penang. One-port negative Oscillator using IMPATT or Gunn diodes. Negative resistance device is usually a biased diode. Oscillation
Professor Syed Idris Syed Hassan
Sch of Elect. & Electron Eng
Engineering Campus USM
Nibong Tebal 14300
Negative resistance device is usually a biased diode. Oscillation
occurred whence ZL= -Zinwhich implies
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
Use the fact that
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
For passive load
By substituting ZT=Zin + ZL, the stability equation reduces to
Where Zin = Rin + j Xin
ZL =RL + jXL
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
Usually we have to choose
For steady -state
We can proved that
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.
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
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= -84 - j1.9 W
Using a transmission line to match a resistive load, thus we have a length of 0.241 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
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.
Equivalent series impedance
Where N =coupling factor/turn ratio
Q=R/woL (unloaded resonator)
Ratio of unloaded to external Q is given by
RL=2Zo for loaded resistance
= Zo for l/4 transmission line
Reflection coefficient looking on terminated microstrip feedline towards resonator is given by
Q can be determined by simple measurement of reflection coefficient
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.
2. Choose a point Gin
Inside the instability area
Calculate the Gout and Gin = GL using this formula
We obtain Gout = 10.7/132o. This corresponding to
So we have
d1=0.034l l1=0.193 l
Or d1=0.429l l1=0.307l
Resonator should be placed at zero or 180o of phase from the transistor. So we have either 0.181 l (zero phase) or 0.431 l (180o phase)
d2= 0.181 l
Or = 0.431 l
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.
Parallel impedances for Rp , Lp , and Cp can be written as
The transfer function of the oscillator is given by
Then substitute for Zp , we have
Where fo=oscillation frequency
And the gain condition (Barkhausen) for oscillation is gmRp=1
Thus, any changes will result
In the oscillator model, the noise source is Rp .The noise current produced is
k=Boltzman const , T = absolute temp.
Since gm= 1/Rp and Iout= gm* Vin , the noise current can be transferred to input and hence Vin can be written as
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
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.
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.
As in previous example
Maximum oscillation frequency
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
Condition for oscillation
S11’>1 and S22’>1
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
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.