Title: RF
1RF Microwave Fundamentals
2Basic 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
-
3Electromagnetic 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.
4Range 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)
5Some Terms You Will Hear
- dB
- dBm
- Impedance
- Return Loss (RL)
- Insertion Loss (Cable Loss)
- VSWR
- DTF
- Watts
6Linear 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.
7Bel
- A bel is defined as the logarithm of a power
ratio. - Po
- bel log
- Pi
8Decibel (dB)
- Decibel (dB) is a logarithmic unit of relative
power measurement that expresses the ratio of two
power levels. -
- Po
- dB 10 log
- Pi
9dBm
- dBm is the decibel value of a signal compared to
1 m w.
103 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.
12Basic Concept
Length
13Wavelength (?)
- VC
- (?)
- er f
- Where VC velocity of propagation through
air - er relative dielectric constant
- f frequency of oscillation
14Velocity of Propagation
- Electromagnetic energy travels at the speed of
light.
15Time Domain and Frequency Domain
16Transmission 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 )
17Impedance
- 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
18Different Types Transmission Line
- There are many different types of transmission
lines and we will talk about three of them. - Coaxial
- Waveguide
- Microstrip
19Coaxial Cable
20Waveguide
- Waveguide is a hollow, conducting tube, through
which microwave frequency energy can be
propagated.
21Microstrip Transmission Line
22Characteristic Impedance of Coax
For a lossless line RG0
23Characteristic Impedance
24Propagation Modes of Coax
- Patterns set up by electric and magnetic fields.
25Cutoff 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.
26Velocity of Propagation
- In free space C 3x108 m/sec
- Wavelength ? C/f
- Where f frequency (Hz)
- Z
27Relative Velocity Constant (k)
- k (1/ eR)
- for Teflon eR 2.04
- k (1/ 2.04) 0.7
28Phase 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.
29Well Matched Transmission Line
- If Z0 ZL
- then P0 PL
- No reflection
- Therefore PL PI
30Poorly Matched Transmission Line
- If ZL ? Z0
- then PL ? PI
- Reflection is
- present
- Therefore PL PI - PR
-
31Example
- Short at the end of the line
32SWR Vs Impedance
- ZL ? 0, ZL ? ? and ZL ? Z0
33VSWR
- Voltage Standing Wave Ratio (VSWR)
- Emax ER EI
- VSWR
- Emin ER - EI
- ER
- G(reflection coefficient)
- EI
34Reflection Terms Relationships
35Reflection
36Reflection Coefficient
- Reflection coefficient is the ratio of the
reflected signal to the incident signal. - ZL - Z0
- ER/Ei ? ? ??
- ZL Z0
37Mismatch
- 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.
38Basic Measurements
- Transmission Loss/Gain Pout/Pin
- Return Loss Preflected/Pin
39Transmission Measurement
40Calculating dB Difference
41Power Gain
- Gain is the ratio of the output power level of an
amplifier to the input power level to that
amplifier. - Po
- Gain
- Pi
42Transmission Measurement (Loss/Gain Measurement)
- Transmission Power Gain 20 log (Vo/Vi)
43Making 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).
44Measure Incident Power
- Using detector directly on the test port.
45Measure Output Power
46Transmission Measurement Errors
- Calibration Error
- Test Port Match
- Detector Match
- Using Adapters
47Calibration Error
48Determining Calibration Error
49Test Port Match Error
50Detector Match Error
51Calculating the Errors
52Error Calculation
53Error Example
54Error Calculation
55Maximum Effect
56RSS
57Total Error
58What happens when you add an adapter?
59Example 1
60Example 2
61Improving 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.
62Return Loss
- Return Loss Measurements
- Uncertainty analysis
63Return Loss Measurements
- Problem How do you separate reflected
- signal from incident signal
64Solution 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.
65Solution to RL Measurements
- Directional Devices Couplers (Coaxial and
Waveguide), Bridges, Autotesters
66Making a Return Loss Measurement
- Two requirements when measuring return loss
- Separation of incident and reflected signal
- Establish a 100 reflection reference
67100 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
68100 Reflection Reference
- The Average of an Open Short represents a
true 100 reflection.
69Return Loss Block Diagram
70Errors to Consider
- Directivity
- Test port match
- Termination error
71Calculating Directivity
- Directivity 20 log ( Vin/ Vout) dB
- Example Vin 1 Volt, and Vout 10mV
- Directivity 20 log ( 1/ .01) 40 dB
72Test Port Match
73Termination Error
- Errors in Return Loss
- Termination Error The additional reflection that
an imperfect termination causes.
74Termination Error
75Calculating the Errors
- Directivity Error
- Test Port Match Error
- Termination Error
- ?
- Do it exactly the same way as you did
transmission loss.
76Calculating 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
77Calculating 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
78Error Signal Return Loss (Reflection)
79Calculating 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)
80Return 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
81Measured 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)
82Measured 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)
83Error 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
84Input 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
85Input 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
-
-
86Example 3
87Example 4
88Have We Forgotten Something?
- Instrumental Errors
- Connector Repeatability
89Instrumental 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
90Connector 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
91Summary
92S Parameters VNA Measurement Fundamentals
93S Parameters
94S Parameters
95S 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)
96Diagram for S-Parameters
97Impedance Components
The relationship between the reflection
coefficient and the impedance on a transmission
line
98Smith Chart
99Impedance Components
- The impedance components in the Smith chart are
- The resistive components
- The reactive components
- A- Inductive
- B- Capacitive
100Constant Resistance Circles
101Inductive Reactance Circles
102Capacitive Reactance Circles
103Using Smith Chart
104Whats 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.
105What is phase?
t
These two signals have the same magnitude but are
90 degrees out of phase!
106Phase
- 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.
107What 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
!!
108How does a VNA display the S-parameters?
Log Magnitude and Phase
109Another VNA Display Mode
Smith Chart
110VNAs and Calibration
111VNA 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
112Without 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
113Error 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
114Error Vectors
115Error Vectors
116How 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
117How 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.
118ALL MEASUREMENT ARE REFERENCED
TO A STARTING POINT
START HERE
PHASE MEASUREMENTS BEGIN BY UNDERSTANDING WHERE
THE REFERENCE PLANE IS
POINT IS THE REFERENCE PLANE
119WHY 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.
120Systematic 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.
121Corrected S-parameters
122Calibration - (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
123Calibration 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
124VNA 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
125Uncertainty Curve
126Exact 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
127Measurement Uncertainty Exercise
128Common Microwave Devices
129What do our Customers manufacture?
- Amplifiers
- Mixers
- Power Dividers
- Power Splitters
- Combiners
-
- Couplers
- Circulators
- Isolators
- Attenuators
- Filters
130Amplifier
- 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
-
131Match and Gain
- Use the Transmission/Reflection Measurement mode
of the VNA to measure these parameters - Input match S11
- Output match S22
- Gain S21
132Noise
- We are interested in specific man-made signal
- But there are some unwanted signals combined with
our desired signal. - Thermal Noise
133Noise 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
134Noise Figure
- Noise can be expressed in Noise Figure which is
the logarithmic equivalent of Noise Factor. - Si/Ni
- NF 10 log
- So/No
135Noise Figure Measurement
136Linearity
- 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
1371-dB Compression Point
138Gain 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
139Swept Frequency Gain Compression
140Swept Power Gain Compression
141Third-order Intercept Point (TOIP)
142TOIP
- Third-order intercept point (TOIP)
143Intermodulation Products
- Understanding the dynamic performance of the
receiver requires knowledge of intermodulation
products (IP). - How intermodulation is created?
- What are the intermodulation products?
144Intermodulation (Continued)
- Frequencies causing problem
- Overdriven amplifier or receiver
145IMD/TOI Measurement Setup
146IMD Measurements
147TOI Measurement
148Mixer
- 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)
149Conversion Gain/Loss, Isolation Port Matches
150Mixer IMD Measurement
151Power 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
152Power 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
-
153Combiner
- A Combiner is a passive RF device used to add
together, in equal proportion, two or more RF
signals.
154Coupler
- Directional coupler
- Bidirectional coupler
- A C
-
- B
155RF 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.
156Applications of hybrids
- Combining two signal sources
157Circulator 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.
158Multi-port Devices
159Attenuator
- An Attenuator is a RF component used to make RF
signals smaller by a predetermined amount, which
is measured in decibels.
160Dynamic 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.
161Attenuator Measurements
162Attenuator Measurements
163Filter
- 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
164Filter Measurements