RF

1
RF Microwave Fundamentals

• Jan 2006
• Anritsu Korea

2
Basic Fudamentals

• Definition of Terms
• What Does RF Mean?
• Basic Concepts
• Transmission Lines
• Coaxial Cable
• Waveguide
• Transmission Line Theory
• Transmission measurements and error analysis

• Return Loss measurements and error analysis
• Advanced Measurement Techniques (air lines)
• S Parameters VNA measurement fundamentals
• Common Microwave Devices and measurements
• Synthesizer related RF Concepts

3
Electromagnetic Spectrum

• RF Radio Frequency. A general term used to
  describe the frequency range from 3 kHz to 3.0
  GHz (Gigahertz )
• Microwave. The frequency range 3GHz to 30.0 GHz.
  Above 1 GHz, lumped circuit elements are replaced
  by distributed circuit elements.
• Millimeter wave. The frequency range 30 GHz to
  300 GHz. The corresponding wavelength is less
  than a centimeter.

4
Range of RF Frequencies

• Medium Frequency (300 KHz - 3 MHz)
• High Frequency (HF) (3 - 30 MHz)
• Very High Frequency (VHF) (30 - 300 MHz)
• Ultra High Frequency (UHF) (300 - 3000 MHz)

5
Some Terms You Will Hear

• dB
• dBm
• Impedance
• Return Loss (RL)
• Insertion Loss (Cable Loss)
• VSWR
• DTF
• Watts

6
Linear vs Log

• Some things are very, very large.
• Some things are very, very small.
• It is difficult to express comparison of sizes
  in common units of measure with a linear scale.
• One would not usually express a fleas
  dimensions in miles, for example.

7
Bel

• A bel is defined as the logarithm of a power
  ratio.
• Po
• bel log
• Pi

8
Decibel (dB)

• Decibel (dB) is a logarithmic unit of relative
  power measurement that expresses the ratio of two
  power levels.
• Po
• dB 10 log
• Pi

9
dBm

• dBm is the decibel value of a signal compared to
  1 m w.

10
3 dB rule

• 3 dB means double the power (multiply by 2)
• - 3 dB means halve the power
• (divide by 2)

11
Power Conversion Table

• Some common decibel values and power-ratio
  equivalents.

12
Basic Concept

• Wavelength (?)

Length
13
Wavelength (?)

• VC
• (?)
• er f
• Where VC velocity of propagation through
  air
• er relative dielectric constant
• f frequency of oscillation

14
Velocity of Propagation

• Electromagnetic energy travels at the speed of
  light.

15
Time Domain and Frequency Domain
16
Transmission Line Theory

• Must be applied when line lengths are gt (? / 4 )
• Standard lumped-circuit analysis can be applied
  when the line lengths are ltlt (? / 4 )

17
Impedance

• The impedance of a transmission line can be
  complex Z R jX
• If X is positive, it is called the inductive
  reactance
• If X is negative, it is called capacitive
  reactance
• Impedance plot in a rectangular coordinate

18
Different Types Transmission Line

• There are many different types of transmission
  lines and we will talk about three of them.
• Coaxial
• Waveguide
• Microstrip

19
Coaxial Cable
20
Waveguide

• Waveguide is a hollow, conducting tube, through
  which microwave frequency energy can be
  propagated.

21
Microstrip Transmission Line
22
Characteristic Impedance of Coax
For a lossless line RG0
23
Characteristic Impedance

• Z0 (138/ eR) Log (D/d)

24
Propagation Modes of Coax

• Patterns set up by electric and magnetic fields.

25
Cutoff Frequency

• The lowest frequency at which the next higher
  order mode can propagate is called the cut-off
  frequency of the next higher order mode.

26
Velocity of Propagation

• In free space C 3x108 m/sec
• Wavelength ? C/f
• Where f frequency (Hz)
• Z

27
Relative Velocity Constant (k)

• k (1/ eR)
• for Teflon eR 2.04
• k (1/ 2.04) 0.7

28
Phase of The Signal at One Wavelength

• The phase of the signal at one wavelength
  intervals along the line will be in phase. In
  this instance ?0 is 21 cm at 1 GHz.

29
Well Matched Transmission Line

• If Z0 ZL
• then P0 PL
• No reflection
• Therefore PL PI

30
Poorly Matched Transmission Line

• If ZL ? Z0
• then PL ? PI
• Reflection is
• present
• Therefore PL PI - PR

31
Example

• Short at the end of the line

32
SWR Vs Impedance

• ZL ? 0, ZL ? ? and ZL ? Z0

33
VSWR

• Voltage Standing Wave Ratio (VSWR)
• Emax ER EI
• VSWR
• Emin ER - EI
• ER
• G(reflection coefficient)
• EI

34
Reflection Terms Relationships
35
Reflection
36
Reflection Coefficient

• Reflection coefficient is the ratio of the
  reflected signal to the incident signal.
• ZL - Z0
• ER/Ei ? ? ??
• ZL Z0

37
Mismatch

• Mismatch is a measure of the efficiency of power
  transfer to the load. The percentage of the power
  reflected from the Load.
• 0 dB return loss or infinite VSWR indicate
  perfect reflection by the load.
• Infinite return loss or unity VSWR indicate
• perfect transmission to the load.

38
Basic Measurements

• Transmission Loss/Gain Pout/Pin
• Return Loss Preflected/Pin

39
Transmission Measurement

• Combining Signals

40
Calculating dB Difference
41
Power Gain

• Gain is the ratio of the output power level of an
  amplifier to the input power level to that
  amplifier.
• Po
• Gain
• Pi

42
Transmission Measurement (Loss/Gain Measurement)

• Transmission Power Gain 20 log (Vo/Vi)

43
Making a Transmission Measurement

• Measure incident power going into the device.
• Measure the output power coming out of the
  device.
• The difference in power is transmission loss (or
  gain).

44
Measure Incident Power

• Using detector directly on the test port.

45
Measure Output Power
46
Transmission Measurement Errors

• Calibration Error
• Test Port Match
• Detector Match
• Using Adapters

47
Calibration Error
48
Determining Calibration Error
49
Test Port Match Error
50
Detector Match Error
51
Calculating the Errors
52
Error Calculation
53
Error Example
54
Error Calculation
55
Maximum Effect
56
RSS
57
Total Error
58
What happens when you add an adapter?
59
Example 1
60
Example 2
61
Improving Transmission Loss Measurements

• Use detectors with better match.
• Use attenuator pads or isolators between test
  port and DUT and detector and DUT to diminish
  magnitude of the error signals.

62
Return Loss

• Return Loss Measurements
• Uncertainty analysis

63
Return Loss Measurements

• Problem How do you separate reflected
• signal from incident signal

64
Solution to R L Measurements

• Solution Directional Devices
• Definition A directional device is able to
  separate either the incident or the reflected
  signal from the environment where both exist.

65
Solution to RL Measurements

• Directional Devices Couplers (Coaxial and
  Waveguide), Bridges, Autotesters

66
Making a Return Loss Measurement

• Two requirements when measuring return loss
• Separation of incident and reflected signal
• Establish a 100 reflection reference

67
100 Reflection Reference

• For COAX two references exist
• Open circuit
• Short circuit
• They are 180 out of phase
• For Waveguide two reference can be used
• short circuit and offset short

68
100 Reflection Reference

• The Average of an Open Short represents a
  true 100 reflection.

69
Return Loss Block Diagram
70
Errors to Consider

• Directivity
• Test port match
• Termination error

71
Calculating Directivity

• Directivity 20 log ( Vin/ Vout) dB
• Example Vin 1 Volt, and Vout 10mV
• Directivity 20 log ( 1/ .01) 40 dB

72
Test Port Match
73
Termination Error

• Errors in Return Loss
• Termination Error The additional reflection that
  an imperfect termination causes.

74
Termination Error
75
Calculating the Errors

• Directivity Error
• Test Port Match Error
• Termination Error
• ?
• Do it exactly the same way as you did
  transmission loss.

76
Calculating the Errors

• Calculate how far below the desired signal the
  error signal is (in dB).
• Convert the dB into linear (reflection
  coefficient) form. Use reflection chart or
  calculate.
• GE log-1 -dB error/20
• For worst case, add up all linear terms.
• Sum GE1 GE2 GE3

77
Calculating the Errors

• Effect on the measurement is the linear sum
  adding in phase or subtracting out of phase from
  the nominal return loss of the device under test.
• Measurement GDUT GSUM
• In dB, meas. Max - 20 log GDUT - GSUM
• Min - 20 log GDUT GSUM

78
Error Signal Return Loss (Reflection)
79
Calculating the Errors

• Autotester DUT
• Directivity 40 dB (.01 G) Input/Output Match
  15 dB(.178 G)
• Test Port 20 dB (.1 G) Insertion Loss 1 dB
• Termination Detector
• Return Loss 40 dB (.01G) Return Loss 20 dB
  (.1G)

80
Return Loss Measurement Errors With Termination

• Errors
• A) 2(I.L.) Termination
• 2 dB 40 dB 42 dB (.008G)
• B) 2 (DUT) Test Port
• 30 dB 20 dB 50 dB (.0032G)
• C) Directivity 40 dB (.01G)
• Total Error 0.021G

81
Measured Results For Using Termination

• DUT .178G (15 dB) (1.43 SWR)
• Plus Total Error .021G
• .199G (14.02 dB) ( 1.50 SWR)
• DUT .178G (15 dB) (1.43 SWR)
• Minus Total Error - .021G
• .157G (16.08 dB) (1.37 SWR)

82
Measured Results For Using Detector

• With Detector (as termination)
• A) 2 (I.L.) Detector
• 2 dB 20 dB 22 dB (.079G)
• B) 2(DUT) Test Port 50 dB (.0032G)
• C) Directivity 40 dB (.01G)
• .092G
• Measured Results
• DUT Total Error
• .178G .092G .270G (11.37 dB) (1.74 SWR)
• DUT - Total Error
• .178G - .092G .086G (21.31 dB) (1.19 SWR)

83
Error Signals

• Directivity 40 dB
• Test Port Match 20 dB
• Adapter 36 dB
• DUT 15 dB
• A- Effective Directivity
• Directivity 40 dB (.01G)
• Adapter 36 dB (.0158G)
• Minimum Effective Directivity
• Autotester 40 dB .01G
• Plus Adapter Error .0158G
• .0258? 31.77 dB
• B- Effective Test Port Match
• Autotester 20dB (.1G)
• Adapter 36 dB (.0158)
• Minimum Effective Test port Match
• Autotester 20dB .1G
• Plus Adapter error .0158G
• .1158G 18.73 dB

84
Input Match Errors Due to Sweeper Output and SWR
Autotester Input Match

• Effective Input Match
• dB G
• Sweeper Input Match 16 .159
• Autotester Input Match 20 .10
• Effective Input Match 11.7 dB .259
• 11.7 dB Effective Input
• IL 6.5 dB

85
Input Match Error Signal

• Error DUT IL Input IL DUT dB G
• 15 dB 6.5 dB 11.7 dB 15
  dB 54.7 .00185
• Error Analysis dB G
• Directivity 40 .01
• Test Port
• 2(DUT) Test Port 50 .0032
• Input 54.7 .00185
• Total Error .01505
• DUT 15 dB .178
• Plus Error .01505
• .1931 14.28 dB
• DUT 15 dB .178
• Minus Error - .01505
• .1630 15.78 dB

86
Example 3
87
Example 4
88
Have We Forgotten Something?

• Instrumental Errors
• Connector Repeatability

89
Instrumental Errors

• Signal source harmonics
• Network Analyzer/Detector deviation from
  logarithmic response (.01 dB per dB of
  measurement)
• Readout Error (manual .03 to .1 dB, automated .01
  dB)
• Signal source power and frequency stability

90
Connector Repeatability

• APC-7 Typically 0.02 dB
• N Typically 0.03 dB
• SMA Typically 0.04 dB
• K Typically 0.035 dB
• V Typically 0.045 dB

91
Summary
92
S Parameters VNA Measurement Fundamentals
93
S Parameters

94
S Parameters
95
S Parameters Defined

• S11 Forward Reflection (b1/a1)
• S21 Forward Transmission (b2/a1)
• S22 Reverse Reflection (b2/a2 )
• S12 Reverse Transmission (b1/a2)
• All are Ratios of two signals - (Magnitude and
  Phase)

96
Diagram for S-Parameters
97
Impedance Components
The relationship between the reflection
coefficient and the impedance on a transmission
line
98
Smith Chart
99
Impedance Components

• The impedance components in the Smith chart are
• The resistive components
• The reactive components
• A- Inductive
• B- Capacitive

100
Constant Resistance Circles
101
Inductive Reactance Circles
102
Capacitive Reactance Circles
103
Using Smith Chart
104
Whats the difference between a VNA and a Scalar
Analyzer?

• A Vector Network Analyzer not only measures the
  magnitude of the reflection or transmission, but
  it also measures its PHASE.
• A Scalar Network Analyzer uses a diode to convert
  energy to a DC voltage. It can only measure
  magnitude with limited dynamic range.
• A Vector Analyzer uses a tuned receiver followed
  by a quadrature detector, so phase can be
  measured. Ratio measurements and the benefits of
  the heterodyne process all contribute to over-all
  accuracy and dynamic range.

105
What is phase?
t
These two signals have the same magnitude but are
90 degrees out of phase!
106
Phase

• Using phase information, one can calculate the
  electrical delay through a device.
• Analyzing the variation of phase shift through a
  device with respect to frequency, one can
  calculate group delay.
• Group delay is one cause of distortion in voice
  transmission and bit errors in digital
  transmission systems.

107
What happens when two equal signalswhich differ
by 180 degrees are summed?

• The resultant depends on their relative
  amplitudes
• If the amplitudes are equal - They completely
• cancel -
• This is not hypothetical - When a full
  reflection
• occurs at the end of a transmission line, all
  of the
• incident energy is reflected back to the
  generator
• This causes high standing waves
• Depending where you look along the line,
• you could see ZERO or Twice the loaded Voltage
  !!

108
How does a VNA display the S-parameters?
Log Magnitude and Phase
109
Another VNA Display Mode
Smith Chart
110
VNAs and Calibration
111
VNA Test Set and Source
Source
Transfer Switch
Power divider
Rear Panel Reference Loops
a1
a2
40dB Step Attenuator
4 Samplers
Coupler
b2
b1
Port 1
Port 2
DUT
112
Without calibration a VNA cannot make accurate
measurements

• Calibration means removing errors
• Types of errors to deal with
• Random Errors (i.e. Connector Repeatability)
• Cannot be calibrated out, due to randomness.
• Systematic Errors
• CAN be reduced via calibration
• Transmission and Reflection Frequency Response
  Errors
• Source and Load Match Errors
• Directivity and Isolation (Crosstalk) Errors

113
Error Vectors

• Once the error vector is known (Mag. Phase)
• It can be vectorially added to the raw VNA
  measurement
• Resultant is the actual DUT performance!

error coefficient
raw VNA measurement
actual DUT performance
x
114
Error Vectors
115
Error Vectors
116
How to Calibrate-

• To reduce the systematic errors for both ports
  (Forward and Reverse), a 12 term calibration is
  required.
• Open Short Load Through (OSLT)
• The most common coax calibration method
• Other calibration techniques
• LRL, LRM, TRM, Offset Short...
• Exercise Good Techniques for best results
• Practice/Care/Knowledge/Clean Parts

117
How does calibration work?

• The VNA measures KNOWN standards.
• It will compare the measured value to the known
  value, and calculate the difference.
• The difference is the error. It will store an
  error coefficient (Magnitude and Phase) at every
  frequency/data point, and use it when making
  measurements.

118
ALL MEASUREMENT ARE REFERENCED
TO A STARTING POINT
START HERE
PHASE MEASUREMENTS BEGIN BY UNDERSTANDING WHERE
THE REFERENCE PLANE IS
POINT IS THE REFERENCE PLANE
119
WHY MUST WE MEASURE PHASE???

• ERROR CORRECTION REQUIRES THAT WE HAVE PHASE AND
  MAGNITUDE INFORMATION EVEN IF WE ARE ONLY
  CONCERNED WITH MAGNITUDE DURING TESTING!
• All four S Parameters are interdependent, so we
  must constantly reverse to compensate for Source
  Match, Load Match, Directivity, Frequency
  Response (Reflection), Frequency Response
  Transmission, and Isolation.

120
Systematic Error

• Transmission Frequency Response
• Reflection Frequency Response
• Source Match
• Load Match
• Directivity
• Isolation (Crosstalk)
• Reduced by Calibration
• These Six Terms on both Ports, yield 12 Term
  Error Corrected Data.

121
Corrected S-parameters
122
Calibration - (Open, Short Load, Thru)

• The most common calibration type is the OSL.

• Open
• Infinite Impedance
• Voltage Maximum
• O degree Phase Reflection
• Reflection Magnitude 1
• Load (Broadband)
• 50 Ohms (match)
• Reflection Magnitude 0

• Short
• Zero Ohms Impedance
• Voltage Null
• 180 degrees Phase Reflection
• Reflection magnitude 1
• Through
• Test ports connected together for transmission
  calibration measurement

123
Calibration OSL Sliding Load

• Due to the difficulty of producing a high quality
  coaxial termination (load) at microwave
  frequencies, a sliding load can be used at each
  test frequency to separate the reflection of a
  somewhat imperfect termination from the actual
  directivity
• Broadband measurements required high accuracy
  must use 12 Term sliding load calibration

124
VNA Measurement Uncertainties

• The quality of a VNA measurement can be
  affected by the following
• The Quality of the Calibration Standards
• Error Correction Type used 12 Term, 1 Path 2
  Port, and etc.
• Dynamic Range of the measurement system (VNA)
  IFBW, Averaging and etc.
• Cable stability and Connector repeatability

125
Uncertainty Curve
126
Exact Uncertainty

• A Windows based program is available to help
  obtain the uncertainty data that is appropriate
  for the customers specific application.
• CDROM part number 2300-361
• Application Note 11410-00270

127
Measurement Uncertainty Exercise
128
Common Microwave Devices
129
What do our Customers manufacture?

• Amplifiers
• Mixers
• Power Dividers
• Power Splitters
• Combiners

• Couplers
• Circulators
• Isolators
• Attenuators
• Filters

130
Amplifier

• An Amplifier is an active RF component used to
  increase the power of an RF signal.
• Four fundamental properties of amplifiers are
• Input/Output Matches
• Gain
• Noise figure
• Linearity - 1 dB Compression point
• Small signal in ? Big signal out

131
Match and Gain

• Use the Transmission/Reflection Measurement mode
  of the VNA to measure these parameters
• Input match S11
• Output match S22
• Gain S21

132
Noise

• We are interested in specific man-made signal
• But there are some unwanted signals combined with
  our desired signal.
• Thermal Noise

133
Noise Measurement

• There are many ways to express noise.
• Noise may be expressed in Noise Factor which is
  defined as the input signal-to-noise ratio to the
  output signal-to-noise ratio.
• Si/Ni
• F
• So/No

134
Noise Figure

• Noise can be expressed in Noise Figure which is
  the logarithmic equivalent of Noise Factor.
• Si/Ni
• NF 10 log
• So/No

135
Noise Figure Measurement
136
Linearity

• Linearity is a measure of how the gain variations
  of an amplifier as a function of input power
  distorts the fidelity of the signal.
• Output power VS Input power of an amplifier

137
1-dB Compression Point

• Input signal (dBm)

138
Gain Compression

• Traditionally, power meter is used for this
  measurement tedious procedure
• VNA can now be used very quick and simple
• Two VNA approaches are available
• Swept Frequency Gain Compression
• Swept Power Gain Compression

139
Swept Frequency Gain Compression
140
Swept Power Gain Compression
141
Third-order Intercept Point (TOIP)
142
TOIP

• Third-order intercept point (TOIP)

143
Intermodulation Products

• Understanding the dynamic performance of the
  receiver requires knowledge of intermodulation
  products (IP).
• How intermodulation is created?
• What are the intermodulation products?

144
Intermodulation (Continued)

• Frequencies causing problem
• Overdriven amplifier or receiver

145
IMD/TOI Measurement Setup
146
IMD Measurements
147
TOI Measurement
148
Mixer

• A Mixer is a three-port component used to change
  the frequency of one of the input signals.
• Fundamental properties of mixers are
• Conversion gain/loss
• Port Match
• Isolation
• Intermodulation Distortion (IMD)

149
Conversion Gain/Loss, Isolation Port Matches
150
Mixer IMD Measurement
151
Power Divider

• A Power Divider (also called three-resistor power
  splitter) is a bi-directional device that equally
  divides an RF signal with a good match on all
  arms.
• Input
• Output 1 Output 2

152
Power Splitter

• A Power Splitter (also called two-resistor power
  splitter) is a passive RF device that equally
  divides an RF signal into two RF
  signals. Output 1
• Input
• Output 2

153
Combiner

• A Combiner is a passive RF device used to add
  together, in equal proportion, two or more RF
  signals.

154
Coupler

• Directional coupler
• Bidirectional coupler
• A C
• B

155
RF Hybrid Coupler

• The RF hybrid coupler is a device that will
  either
• (a) split a signal source into two directions or
• (b) combine two signal sources into a common
  path.

156
Applications of hybrids

• Combining two signal sources

157
Circulator and Isolator

• A circulator is a passive junction of three or
  more ports in which the ports can be accessed in
  such an order that when power is fed into any
  port it is transferred to the next port, the
  first port being counted as following the last in
  order.
• An isolator is a 3-port circulator with the third
  port terminated with a load so that power can
  only be transferred in one direction from the
  first port to the second port.

158
Multi-port Devices
159
Attenuator

• An Attenuator is a RF component used to make RF
  signals smaller by a predetermined amount, which
  is measured in decibels.

160
Dynamic Range

• Dynamic Range is basically the difference between
  the maximum and minimum signals that the receiver
  can accommodate. It is usually expressed in
  decibels (dB).
• It is essential that the measurement instrument
  has sufficient dynamic range to accurately
  characterize an attenuator.

161
Attenuator Measurements
162
Attenuator Measurements
163
Filter

• A Filter transmits only part of the incident
  energy and may thereby change the spectral
  distribution of energy
• High pass filters transmit energy above a certain
  frequency
• Low pass filters transmit energy below a certain
  frequency
• Band pass filters transmit energy of a certain
  bandwidth
• Band stop filters transmit energy outside a
  specific frequency band

164
Filter Measurements