RF BASİCS- mikrodalga elektroniği

RF/MICROWAVE BASICS

by

Hakan P. Partal

RF BASICS

OUTLINE

•Electromagnetic Wave Properties

•High Frequency Voltage, Current, and Power

•Forward and backward travelling waves

•Impedance

•Network parameters -- S parameters; Reflection, Insertion Loss, Isolation, Phase

•Microwave circuit measurements.

RF BASICSElectrical energy Electrical energy Electrical energy Electrical energy

� Flows as current along a conductor, when a voltage is applied A bunch of electrons (negative charges) move through a conductor toward region of positive potential in response to an electric field. (For an electric current of 1 ampere, 1Coulomb of electric charge (which consists of about 6.242 × 1018

electrons) drifts every second through any imaginary plane, through which the conductor passes. )

� If the applied voltage is sinusoidal the direction of electron flow changes back and forth – alternating current (AC)

� Travels in the air as invisible waves.

� In a typical wireless system, the electrical energy starts out as current flowing along a conductor, gets changed into waves traveling in the air, and then gets changed back into current flowing along a conductor again.

0V

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-1V

time

I

I

RF BASICS

� Moving electrons can be treated as electromagnetic waves

� An electromagnetic wave has

frequency (f),

wavelength (λλλλ), velocity (v)

� A medium has

permitivity or dielectric constant (εεεεr or Dk)characteristic impedance (Z)

εεεεr

� Frequency :cycles per second (Hz).

(F=1/Time)

900 MHz exhibits 900 million

ups and downs in a single second.

Wow!

� Distance = Velocity x Time

⇒ In air, EM waves travel at the speed of light,

⇒ C (3x108 m/sec).

� Wavelength (λλλλ) = C x Time = C x 1/F = C/F (in air)

EM WAVE PROPERTIES

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1 sec

2 Hz

EM WAVE PROPERTIES

Wavelength is a function of velocity, frequency, and medium:

Wavelength (λλλλ) = velocity / Frequency = ( C / √√√√Dk ) / F (m) general definition

� Dk=1 in air

� When Dk is high, Wavelength is shorter and more cycles of waves in the same physical distance . EM wave velocity gets slower.

� When Frequency is high, wavelength is shorter

CATS: Higher Frequency ( more movement cycles)

Small in size physically

BUT, large electrically !

ELEPHANTS: Lower Frequency (less movement cycles)

Large in size physically

But, small electrically :–(

EM WAVE PROPERTIES� 1 wavelength : 1λ=360°

� 800MHz signal in a Rogers 3003 (εr=3) board, � λ=8.52”⇒ 24 mils = 1o

� 2GHz signal in a Rogers 3003 (εr=3) board,� λ=3.41”⇒ 10 mils = 1o which is electrically more significant

• Higher the frequency, smaller the wavelength,

can leak thru small gaps !

• Wavelength = c / (F √√√√ εr ) 90o, π/2

0o

180o, π

270o

360o

270

0

+1V

-1V

λ/2

180o

λ

360o

λ/4

90o

MICROWAVE CIRCUIT EXAMPLES

� Couplers are designed based on ¼ wavelength (λ/4). Can be smaller in size if used higher Dk materials,

Smaller in length at higher frequencies

� Also, other resonant circuits such as filters, power combiners, dividers, antennas, etc.

� Delay lines apply electrical delay for wave propagation. They can be smaller with higher Dk materials.

FREQUENCY SPECTRUM

MICROWAVE MEASUREMENTS

S-PARAMETERSCommon way to represent network parameters using complex coefficients:

� magnitude & phase

� Real & imaginary

� dB & phase

2 Port Network

a1

b1

a2

b2

S21

S12

S22S11

Matrix notation: Sij

Port

measured

Port

excited

S11=RL @ port 1

S21=IL from port 1 to 2

S12=IL from port 2 to 1

S22=RL @ port 2

Port 1 Port 2

SCATTERING PARAMETERS

Z02

Z02

Two-port

network

FWD wave

BWD wave

SCATTERING PARAMETERS

S PARAMETERS

SCATTERING PARAMETERS MULTIPLE REFLECTION EFFECTS

b1

RF POWER MEASUREMENTS � dB� At low frequencies, voltage and

current are measured. These parameters are difficult to measure at higher frequencies so power is measured.

� In microwave world the dB scaleis used commonly.

� This scale “compresses” the data range.

0 100 200 300 400 500 600 700 800 900 10000

5

10

15

20

25

30"Com pres s ion" Us ing Logarithm ic S c ale

X

10*Log(x)

Power Out/In

dB

dB

� dB is a relative quantity based on the ratio of two numbers (powers in microwave analysis).

� dB = 10Log10(Pout/Pin)

� Log10(AxB) = Log10 (A)+Log10 (B)

� Ex. A coupler has 1W applied to input (port 1) and 1/2W measured at Output Ports (Ports 2&3). What is the output power in dB?

P(dB) = 10Log10(0.5W / 1W)

= 10Log10(0.5) = -3dB

Ratio dB Value

1/1000 -30

1/100 -20

1/10 -10

½ -3

1 0

2 3

10 10

100 20

1000 30

100x 2x1mW 100mW 200mW

20dB 3dB+ = 23dB

dBm

� dBm = 10Log10(Pout/1mW)

where Pin is defined as 0.001W=1mW

� This allows us to represent an actual power using the dB scale as opposed to relative powers.

� When a system has 1mW at the input, the output power is described in dBm.

1mW Pout

= 10Log10(Pout/1mW)

Pout is represented in dBm.

Ex. –Convert 200mW to dBm:

10Log10(200mW/1mW) = 23dBm

Power(mW) dBm

0.001 -30

0.01 -20

0.1 -10

1 0

10 10

100 20

1000 30

SYSTEM IMPEDANCE

� System impedance in microwave

circuits is generally 50ohm.

� Components and cables that

connect them have characteristic

impedance of 50ohm.

� Equipment is generally designed

with 50ohm interfaces.

� If all components of the system

are NOT 50ohm, the system will

not operate optimally.

Test

Equipment.

Microwave

Device

50ohm cable

50ohm ports

50ohm ports

CHARACTERISTIC IMPEDANCE

� Electric field is generated by charges � E-field (V/m)

� Magnetic field is generated by current (moving charges)-

H-field (A/m) (Right hand rule)

� Characteristic Impedance of a medium “Z” is defined as E / H

� Free Space intrinsic impedance, Zair = η = 377ohm.

� In transmission lines, Z is determined by geometry and materials used.

ε2

ε1

Top GND plane

Bottom GND plane

TL

TRANSMISSION LINES (TL)

� A TL carries a microwave signal in a guided medium

� EM waves can travel in the air (antenna radiation)

� Some TL examples are Coaxial cables, Striplines, Microstrip lines, waveguides, etc.

� TL parameters: Frequency range, Bandwidth, power handling, loss, size, manufacturing process, etc.

Stripline Microstrip line Coaxial cable

TL

Dielectric substrate

GND plane

ε1

E-lines

H-lines

ε2

ε1

Top GND plane

Bottom GND plane

TL

ε1

Outer cond.

IC

air

MICROWAVE MEASUREMENT PARAMETERS

Return Loss

Insertion Loss

Isolation

Phase

MICROWAVE MEASUREMENT PARAMETERS

Network Analyzer:

-Applies a signal to port#1

-Measures reflected power at port#1

-Measures transmitted power at port#2

Incident

ReflectedTransmitted

Two Port DevicePort 1 Port 2

RETURN LOSS

� It is a relative measure of reflected power

� If characteristic impedance of a transmitted medium different, reflection occurs!

RL (dB) = |10Log10(Preflected/Pincident)|

= -20 log10|S11|

� The larger (Negative) number means better RL (less reflection)

� 20dB of Return Loss means

1% of incident power reflected back.

10Log10(1/100)= -20dB Incident

Wave

Air

Sea

εr=1

ε r=85

Reflected

Transmitted

INSERTION LOSS

� Loss caused by Reflection

� TLs get hot when power pass through them, some power is lost converted to heat energy

� Losses in the dielectric and copper,

� Losses due to radiation (leakages)

� Some power is intentionally lost due to design needs (e.g attenuators)

IL (dB) = |10Log10(Ptransmitted/Pincident)|

ISOLATION

• When EM wave travels in a poorly confined medium, some power could sneak out.

• If wavelength is small (higher frequency or higher Dk), this leakage is more pronounced.

• Must shield and use GND vias to eliminate leakages.

• Consider a 4 port coupler, some power from Input 1 will show up at Input 2

Isolation (dB) = 10Log10(P2 / Pincident)

• When there is a Good Isolation, P2=0 and ISO= -Infinity

• The larger (Negative) number represents the better isolation

4 Port

Coupler

Input 1

Input 2

OUT

Load

PHASE

� Corresponds to the time or distance travelled

� Gives information about the length of a transmission line

� Can measure the time difference between two signals at the same frequency.

Phase = 360 x(∆t / t(1cycle) ) (degrees)1 wavelength = 360o = 2π

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∆t

time0V

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Phase

2π360o

π180o