MICROWAVE BENCH MICROWAVE BENCH MEASUREMNT SU

PROF. A. BHATTACHARYADEPT. OF E & ECE

INDIAN INSTITUTE OF TECHNOLOGYKHARAGPUR – 721 302KHARAGPUR 721 302

Slotted Line with Carriageg

Components used in Microwave LaboratoryMicrowave Laboratory

Some more componentsp

Microwave Bench

A Gunn based Bench

THE MICROWAVE BENCH

Waveforms in Bench

Detector

Rectangular Waveguideg g

Measurement of unknown Load Impedance

(1)Measurement of VSWR on line

(2)Measurement of lmin (distance fromload to 1st voltage minima)load to 1 voltage minima)

These two information sufficient fordetermination of ZL

M it dMagnitude

Voltage minima occurs wheng

where θ is phase of ReflectionCoefficientCoefficient

So, θ= π + 2βlmin

Voltage minima repeats every λ/2 along lineS b l ti h ld f l + λ/2So, above relation holds for any lmin + n λ/2

l = 0

Bench MeasurementIn a measurement lab,) h l d l d la) A short placed at load plane

b) From arbitrarily positioned scale on slotted line,recorded voltage minima→Z = 0.2 cm, 2.2 cm, 4.2 cm., ,

c) Short removed and unknown load put

d) SWR measured 1 5d) SWR measured 1.5

e) Voltage minima at Z = 0.72 cm, 2.72 cm, 4.72 cm

f) Why not voltage maxima→

sharply definedsharply defined

Solution• Voltage minima repeats every λ/2

S λ 2(2 2 0 2) 4So, λ = 2(2.2 – 0.2) = 4 cm.• Reflection coefficient and input impedance alsop prepeats every λ/2.• We can consider load terminals at minima of• We can consider load terminals at minima ofstep (b)

• Let load at 4.2 cm.

• Nearest minima under load at 2 72 cm• Nearest minima under load at 2.72 cm.

Lmin = 4.2 – 2.72 = 1.48 cm = 1.48/4 = 0.37 λ

How do you do the calculation by smith Chart?

• Step I: Locate the point where r=1.5 circle cuts real axis of pSmith Chart (point A)

h ???Why???

Left or Right point???

Voltage Maxima and minima in Smith Chartg

)(1)( zZ ρ+′Variation of Line Impedance)(1)()(

zzZ

ρρ

−=′•Variation of Line Impedance

If l li ( ) h•If we move along line, ρ(z) changes but ρ0 (load reflection coefficient) does not changedoes not change 

•If we move along Transmission LineIf we move along Transmission Line, we cross real axis at two points.

Voltage Maxima and minima in Smith Chart (contd.)(contd.)

Line Impedance is real at these two• Line Impedance is real at these two points

•Reflection Coefficient is also real at•Reflection Coefficient is also real at these two points

•One value is +|ρ0| other ‐|ρ0|

||1||1

0

0max ρ

ρ−+

=′R

One value is +|ρ0|, other  |ρ0|

•One corresponds to Impedance Maxima (Voltage Maxima, Current  || 0ρ( g ,Minima)

•Another to Impedance Minima  ||1 0ρ−=′R

(Voltage Minima, Current Maxima)

•Note VSWR||1 0

min ρ+=R

How do you do the calculation by smith Chart?

Step 2:p

Draw constant VSWR circle with radius OA

Step 3:Step 3:

Where is the short at Smith Chart? Voltage minima i h hexists there. Locate that as C

• Step 4

– Load is 0.37      from the voltage minimaλ

– Which way to go?

– Note: )2( lj βθ −– Note: 

– To move to generator, we go clockwise (why?) 

)2( lje βθ

– So, to reach load, we should go anticlockwise

Step 5

Reach D on the Smith chart periphery

• Step 6: – Join DO, it intersects VSWR circle at E,

Step 7:

Read impedances of E This is the unknownRead impedances of E. This is the unknown impedance

40950' j

Ω+=

+=

205.47

4.095.0'

jz

jz

L

L

Close agreement with analytical calculationsClose agreement with analytical calculations