Calculating Reflection and VSWR
in Antennas
Dr. Farahmand
Updated: 10/20/14
Antenna
o  How much RF energy the antenna
can radiate or emit?
Radiation
Pradiated
Power
Forward
n  This is due to its radiation resistance
(Rr) (resistive characteristic of the
antenna – imaginary part: jX)
n  The ohmic resistance (Ro)of the
antenna acts as physical resistance,
converting energy to heat)
ZL
Power
Reflected
Zo
o  Radiate Power Pt: I2xRr
Zin
RF Current
at the
feedline
Remember
How Electromagnetic Waves Work
o  So if waves travel what happens when they hit an
object?
n
n
RF signal creates disturbances in the media
Some of the signal reflects when the standing wave hits an
object (some get observed)
o  Reflected wave (BLUE)
o  Incident wave (RED)
o  Resulting Standing wave (BLACK)
Between source and
Antenna
http://www.walter-fendt.de/ph14e/stwaverefl.htm
Voltage Standing Wave Radio
(VSWR)
o
Determines loss of forwarded radiation due to returned power
n
Note that the loss can be compensated by high power àDamage
the transmitter
o
o
VSWR results from mismatched impedance
To calculate the VSWR, first calculate the reflection coefficient:
o
VWSR is represented as VWSR:1;
n
o
e.g., 3:1 assuming reflection coefficient is 0.5 – represent how
much mismatch we have!
Based on VWSR we can determine the power loss
n  http://www.microwaves101.com/calculators/872-vswrcalculator
http://www.antennex.com/preview/vswr.htm
Voltage Standing Wave Radio
(VSWR)
o  Determines loss of forwarded radiation due to returned power
§ W
hat is minimum value of COR?
o  VSWR results from mismatched impedance
hort:
CORà
-1 by high power
o § S
The
loss can
be compensated
n  Damage the transmitter
§
O
pen: CORà 1
o  To calculate the VSWR, first calculate the reflection coefficient:
VWSR is represented as VWSR:1; e.g., 3:1 assuming reflection
coefficient
is 0.5 maximum value of VSWR?
§ What
is the
o  Based on VWSR we can determine the power loss
§ n Shortà
Zero
Verify these values: http://www.skyworksinc.com/uploads/
documents/VSWRreturn.pdf
§ Openà
Infinity
o
http://www.antennex.com/preview/vswr.htm
Voltage Standing Wave Radio
(VSWR)
o  Determines loss of forwarded radiation due to returned power
§ W
hat is minimum value of COR?
o  VSWR results from mismatched impedance
hort:
CORà
-1 by high power
o § S
The
loss can
be compensated
n  Damage the transmitter
§
O
pen: CORà 1
o  To calculate the VSWR, first calculate the reflection coefficient:
We want COR = 0
à VSWR = 1
VWSR is represented as VWSR:1; e.g., 3:1 assuming reflection
coefficient
is 0.5 maximum value of VSWR?
§ What
is the
o  Based on VWSR we can determine the power loss
§ n |Γ|=1àInfinity
Verify these values: http://www.skyworksinc.com/uploads/
documents/VSWRreturn.pdf
§ |Γ|=0à1
o
http://www.antennex.com/preview/vswr.htm
Return Loss
o  The return loss of a load is merely the
magnitude of the reflection coefficient
expressed in decibels
Example
o  Consider VSWR of 3:1
n  Find COR
n  Find Return Loss (dB)
n  Find Mismatch Loss (dB)
http://www.microwaves101.com/calculators/872-vswr-calculator
Examples
Bounce Diagram
Assume Vg=60V ; Rg = 100; Zo= 50; L = 1 meter; Vp=2C/3
t=0;
V1
Time Response Voltage
V(z=0.5,t)
V1.ΓL=-6.67
10ns
20-6.
67
=13.3
3
7.5
ns
11.13+0.
74=
13.33- 11.87
2.2
=11.13
12.5
ns
17.5
ns
5 ns
7.5
ns
12.5 ns
15 ns
V1.ΓL.
Γg=
-6.67/3=2.2
25
ns
0.23469
V1.ΓL. ΓL.
Γg=0.74
20
2.5
ns
2.5
ns
20ns
Stables
22.5 ns
L/2
Power Reduction Due to
Reflection
Power Budget
o  Read the handouts
http://www.zytrax.com/tech/wireless/calc.htm#fresnel
Introduction to Power Budget –
A simple Example
o
Assume the following:
n
n
n
n
n
o
Transmitter is transmitting 100mW on channel 1, 802.11b
A, C, D connectors each have a loss of -3dB
Transmitter antenna has an active gain of +12dB
The two antennas are 124 meters away from one another
Ignore the attenuation of the coax cable
Answer the following
n
n
The power in Watts as Receiver Y receives.
Assuming the sensitivity of the receiver antenna is -5dBm, will Y
receive the transmitted information properly?
Transmitter
X
Do it!
A
Coax
Cable
C
D
d
Receiver
Y
802.11b Frequency Band
o
In the United States and Canada there are 11 channels available for
use in the 802.11b 2.4GHz WiFi Frequency range. This standard is
defined by the IEEE.
1
2
3
4
5
6
7
8
9
10
11
2.401
2.404
2.411
2.416
2.421
2.426
2.431
2.436
2.441
2.446
2.451
http://www.moonblinkwifi.com/2point4freq.cfm
2.412
2.417
2.422
2.427
2.432
2.437
2.442
2.447
2.452
2.457
2.462
2.423
2.428
2.433
2.438
2.443
2.448
2.453
2.458
2.463
2.468
2.473