Calculating Reflection and VSWR in Antennas

Dr. Farahmand Updated: 10/20/14

Antenna o  How much RF energy the antenna

can radiate or emit? 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)

o  Radiate Power Pt: I2xRr

RF Current at the feedline

Radiation Pradiated

ZL

Zo

Zin

Power Forward

Power Reflected

Remember How Electromagnetic Waves Work o  So if waves travel what happens when they hit an

object? n  RF signal creates disturbances in the media n  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)

http://www.walter-fendt.de/ph14e/stwaverefl.htm

Between source and Antenna

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 àDamage the transmitter

o  VSWR results from mismatched impedance o  To calculate the VSWR, first calculate the reflection coefficient:

o  VWSR is represented as VWSR:1; n  e.g., 3:1 assuming reflection coefficient is 0.5 – represent how

much mismatch we have! o  Based on VWSR we can determine the power loss

n  http://www.microwaves101.com/calculators/872-vswr-calculator

http://www.antennex.com/preview/vswr.htm

Voltage Standing Wave Radio (VSWR) o  Determines loss of forwarded radiation due to returned power o  VSWR results from mismatched impedance o  The loss can be compensated by high power

n  Damage the transmitter o  To calculate the VSWR, first calculate the reflection coefficient:

o  VWSR is represented as VWSR:1; e.g., 3:1 assuming reflection coefficient is 0.5

o  Based on VWSR we can determine the power loss n  Verify these values: http://www.skyworksinc.com/uploads/

documents/VSWRreturn.pdf

http://www.antennex.com/preview/vswr.htm

§ What is minimum value of COR? § Short: CORà -1 § Open: CORà 1

§ What is the maximum value of VSWR? § Shortà Zero § Openà Infinity

Voltage Standing Wave Radio (VSWR) o  Determines loss of forwarded radiation due to returned power o  VSWR results from mismatched impedance o  The loss can be compensated by high power

n  Damage the transmitter o  To calculate the VSWR, first calculate the reflection coefficient:

o  VWSR is represented as VWSR:1; e.g., 3:1 assuming reflection coefficient is 0.5

o  Based on VWSR we can determine the power loss n  Verify these values: http://www.skyworksinc.com/uploads/

documents/VSWRreturn.pdf

http://www.antennex.com/preview/vswr.htm

§ What is minimum value of COR? § Short: CORà -1 § Open: CORà 1

§ What is the maximum value of VSWR? § |Γ|=1àInfinity § |Γ|=0à1

We want COR = 0 à VSWR = 1

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

L/2

t=0; V1 5 ns

2.5 ns

V1.ΓL=-6.67 10ns

7.5 ns

15 ns

12.5 ns

V1.ΓL. Γg= -6.67/3=-2.2

V1.ΓL. ΓL. Γg=0.74 20ns

25 ns 0.23469

2.5 ns

7.5 ns

12.5 ns

17.5 ns

22.5 ns

20

20-6.67 =13.33

13.33-2.2 =11.13

11.13+0.74= 11.87

Time Response Voltage V(z=0.5,t)

Stables

Assume Vg=60V ; Rg = 100; Zo= 50; L = 1 meter; Vp=2C/3

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  Transmitter is transmitting 100mW on channel 1, 802.11b n  A, C, D connectors each have a loss of -3dB n  Transmitter antenna has an active gain of +12dB n  The two antennas are 124 meters away from one another n  Ignore the attenuation of the coax cable

o  Answer the following n  The power in Watts as Receiver Y receives. n  Assuming the sensitivity of the receiver antenna is -5dBm, will Y

receive the transmitted information properly?

TransmitterX

Coax Cable

A C D ReceiverY

d

Do it!

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 2.401 2.412 2.423 2 2.404 2.417 2.428 3 2.411 2.422 2.433 4 2.416 2.427 2.438 5 2.421 2.432 2.443 6 2.426 2.437 2.448 7 2.431 2.442 2.453 8 2.436 2.447 2.458 9 2.441 2.452 2.463 10 2.446 2.457 2.468 11 2.451 2.462 2.473

http://www.moonblinkwifi.com/2point4freq.cfm