Dr. Vishwani D. Agrawal
James J. Danaher Professor of Electrical and Computer
Engineering
Auburn University, Alabama 36849, USA vagrawal@eng.auburn.edu
http://www.eng.auburn.edu/~vagrawal
Copyright 2008, Agrawal
August 7-13, 2010
Lectures 15-16: TF Testing 1

1.
S. Bhattacharya and A. Chatterjee, "RF Testing," Chapter 16, pages
745-789, in System on Chip Test Arch itectures, edited by L.-T. Wang,
C. E. Stroud and N. A. Touba, Amsterdam: Morgan-Kaufman, 2008.
2.
M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for
Digital, Memory & Mixed-Signal VLSI Circuits , Boston: Springer, 2000.
3.
J. Kelly and M. Engelhardt, Advanced Production Testing of RF, SoC, and SiP Devices , Boston: Artech House, 2007.
4.
B. Razavi, RF Microelectronics , Upper Saddle River, New Jersey:
Prentice Hall PTR, 1998.
5.
J. Rogers, C. Plett and F. Dai, Integrated Circuit Design for High-
Speed Frequency Synthesis , Boston: Artech House, 2006.
6.
K. B. Schaub and J. Kelly, Production Testing of RF and System-ona-chip Devices for Wireless Communications , Boston: Artech House,
2004.
2
Copyright 2008, Agrawal Lectures 15-16: TF Testing

Superheterodyne Transceiver
ADC
LNA VGA
0 °
Phase
Splitter
90 °
LO
ADC
LO
DAC
PA
VGA
0 °
Phase
Splitter
90 °
LO
DAC
RF
Copyright 2008, Agrawal
IF
Lectures 15-16: TF Testing
BASEBAND
3

Zero-IF (ZIF) Transceiver
ADC
LNA
0 °
Phase
Splitter
90
°
LO
ADC
PA
DAC
0 °
Phase
Splitter
90 °
LO
DAC
RF
Lectures 15-16: TF Testing
BASEBAND
Copyright 2008, Agrawal
4


Radio frequency

Mixed-signal

ADC: Analog to digital

Duplexer

LNA: Low noise amplifier

PA: Power amplifier

RF mixer

Local oscillator

Filter

Intermediate converter

DAC: Digital to analog converter

Digital

Digital signal processor
(DSP) frequency

VGA: Variable gain amplifier

Modulator

Demodulator

Filter
5
Copyright 2008, Agrawal Lectures 15-16: TF Testing


Amplifies received RF signal

Typical characteristics:

Noise figure

IP3

Reverse isolation
2dB
– 10dBm

Gain 15dB

Input and output impedance 50 Ω
20dB

Stability factor

Technologies:

Bipolar
> 1

CMOS

Reference: Razavi, Chapter 6.
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
6


Feeds RF signal to antenna for transmission

Typical characteristics:

Output power +20 to +30 dBm

Efficiency

IMD

Supply voltage
30% to 60%
– 30dBc
3.8 to 5.8 V

Gain 20 to 30 dB

Output harmonics – 50 to – 70 dBc

Power control

Stability factor
On-off or 1-dB steps
> 1

Technologies:

GaAs

SiGe

Reference: Razavi, Chapter 9.
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
7


Translates frequency by adding or subtracting local oscillator (LO) frequency

Typical characteristics:

Noise figure

IP3

Gain
12dB
+5dBm
10dB

Input impedance

Port to port isolation

Tecnologies:
50 Ω
10-20dB

Bipolar

MOS

Reference: Razavi, Chapter 6.
8
Copyright 2008, Agrawal
Lectures 15-16: TF Testing


Provides signal to mixer for down conversion or upconversion.

Implementations:

Tuned feedback amplifier

Ring oscillator

Phase-locked loop (PLL)

Direct digital synthesizer (DDS)
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
9


All components of a system are implemented on the same VLSI chip.

Requires same technology (usually CMOS) used for all components.

Components not implemented on present-day
SOC:

Antenna

Power amplifier (PA)
10
Copyright 2008, Agrawal
Lectures 15-16: TF Testing


Basic tests

Scattering parameters (S-parameters)

Frequency and gain measurements

Power measurements

Power efficiency measurements

Distortion measurements

Noise measurements
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
11


An RF function is a two-port device with

Characteristic impedance ( Z
0

Z
0
):
= 50 Ω for wireless communications devices

Z
0
= 75 Ω for cable TV devices

Gain and frequency characteristics

S-Parameters of an RF device

S
11

S
22

S
21

S
12
: input return loss or input reflection coefficient
: output return loss or output reflection coefficient
: gain or forward transmission coefficient
: isolation or reverse transmission coefficient

S-Parameters are complex numbers and can be expressed in decibels as 20 × log | S ij
|
Copyright 2008, Agrawal Lectures 15-16: TF Testing
12

a
1
Port 1
(input) b
1
RF
Device a
2
Port 2
(output) b
2
Input return loss
Isolation
S
11
Output return loss S
22
Gain S
21
S
12
= b
1
/ a
1
= b
2
/ a
2
= b
2
/ a
1
= b
1
/ a
2
Lectures 15-16: TF Testing
Copyright 2008, Agrawal
13

S-Parameter Measurement by Network Analyzer
Directional couplers
DUT
Digitizer a
1 b
1
Directional couplers
Digitizer a
2 b
2
Copyright 2008, Agrawal
Lectures 15-16: TF Testing 14


Example: In an S-parameter measurement setup, rms value of input voltage is 0.1V and the rms value of the reflected voltage wave is 0.02V.
Assume that the output of DUT is perfectly matched. Then S
11

S
11 determines the input match :
= 0.02/0.1 = 0.2, or 20 × log (0.2) = –14 dB.

Suppose the required input match is –10 dB; this device passes the test.

Similarly, S
22 determines the output match.
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
15

21

An amplifier of a Bluetooth transmitter operates over a frequency band 2.4 – 2.5GHz. It is required to have a gain of
20dB and a gain flatness of 1dB.

Test: Under properly matched conditions, S
21 several frequencies in the range of operation: is measured at

S
21
= 15.31 at 2.400GHz

S
21
= 14.57 at 2.499GHz

From the measurements:

At 2.400GHz, Gain = 20 ×log 15.31 = 23.70 dB

At 2.499GHz, Gain = 20 ×log 14.57 = 23.27 dB

Result: Gain and gain flatness meet specification.
Measurements at more frequencies in the range may be useful.
Copyright 2008, Agrawal Lectures 15-16: TF Testing
16


Receiver

Minimum detectable RF power

Maximum allowed input power

Power levels of interfering tones

Transmitter

Maximum RF power output

Changes in RF power when automatic gain control is used

RF power distribution over a frequency band

Power-added efficiency (PAE)

Power unit: dBm, relative to 1mW

Power in dBm = 10 × log (power in watts/0.001 watts)

Example: 1 W is 10 ×log 1000 = 30 dBm

What is 2 W in dBm?
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
17


Multiples of the carrier frequency are called harmonics.

Harmonics are generated due to nonlinearity in semiconductor devices and clipping (saturation) in amplifiers.

Harmonics may interfere with other signals and must be measured to verify that a manufactured device meets the specification.
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
18


Definition: Power-added efficiency of an RF amplifier is the ratio of RF power generated by the amplifier to the
DC power supplied:

PAE = ΔP
 ΔP
RF

P dc
RF
/ P
DC
=
= where
P
RF
(output) – P
RF
(input)
V supply
× I supply

Important for power amplifier (PA).

1 – PAE is a measure of heat generated in the amplifier, i.e., the battery power that is wasted.

In mobile phones PA consumes most of the power. A low PAE reduces the usable time before battery recharge.
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
19


Following measurements are obtained for an RF power amplifier:

RF Input power = +2dBm

RF output power = +34dBm

DC supply voltage = 3V

DUT current = 2.25A

PAE is calculated as follows:

P
RF
(input)

P
RF
(output)
= 0.001 × 10 2/10 = 0.0015W
= 0.001 × 10 34/10 = 2.5118W

P dc
= 3 × 2.25
= 6.75W

PAE = (2.5118 – 0.00158)/6.75 = 0.373 or 37.2%
20
Copyright 2008, Agrawal
Lectures 15-16: TF Testing


An unwanted change in the signal behavior is usually referred to as distortion .

The cause of distortion is nonlinearity of semiconductor devices constructed with diodes and transistors.

Linearity:

Function f(x) = ax + b, although a straight-line is not referred to as a linear function.

Definition: A linear function must satisfy:
 f(x + y) = f(x) + f(y), and
 f(ax) = a f(x), for all scalar constants a
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
21

f(x) f(x) b slope = a x f(x) = ax + b f(x) b f(x) = ax 2 + b x f(x) = ax
Lectures 15-16: TF Testing slope = a x
Copyright 2008, Agrawal
22


Transfer function of an electronic circuit is, in general, a nonlinear function.

Can be represented as a polynomial:
 v o
= a
0
+ a
1 v i
+ a
2

Constant term a
0 v i
2 + a
3 v i
3 + · · · · is the dc component that in RF circuits is usually removed by a capacitor or highpass filter.

For a linear circuit, a
2
= a
3
= · · · · = 0.
Electronic v i v o circuit
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
23


Consider a transfer function, v o

Let v i
= A cos ωt

Using the identities ( ω = 2πf):
 cos 2 ωt = (1 + cos 2ωt)/2
= a
0
+ a
1
 cos 3 ωt = (3 cos ωt + cos 3ωt)/4

We get, v i
+ a
2 v i
2 + a
3 v i
3
 v o
= a
0
+ a
2
A 2 /2 + (a
1
A + 3a
3
A 3 /4) cos ωt
+ (a
2
A 2 /2) cos 2 ωt + (a
3
A 3 /4) cos 3 ωt
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
24

Problem for Solution

A diode characteristic is, I = I voltage. I s s
( e αV – 1)

Where, V = V
0
+ v in
, V
0 is dc voltage and v in is small signal ac is saturation current and α is a constant that depends on temperature and design parameters of diode.

Using the Taylor series expansion, express the diode current
I as a polynomial in v in
.
I
0
– I s
Lectures 15-16: TF Testing
V
Copyright 2008, Agrawal 25


Linear devices:

All frequencies in the output of a device are related to input by a proportionality, or weighting factor, independent of power level.

No frequency will appear in the output, that was not present in the input.

Nonlinear devices:

A true linear device is an idealization. Most electronic devices are nonlinear.

Nonlinearity in amplifier is undesirable and causes distortion of signal.

Nonlinearity in mixer or frequency converter is essential.
Lectures 15-16: TF Testing
Copyright 2008, Agrawal
26


Types of distortion:

Harmonic distortion: single-tone test

Gain compression: single-tone test

Intermodulation distortion: two-tone or multitone test

Testing procedure: Output spectrum measurement
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
27


Harmonic distortion is the presence of multiples of a fundamental frequency of interest. N times the fundamental frequency is called N th harmonic.

Disadvantages:

Waste of power in harmonics.

Interference from harmonics.

Measurement:

Single-frequency input signal applied.

Amplitudes of the fundamental and harmonic frequencies are analyzed to quantify distortion as:

Total harmonic distortion (THD)

Signal, noise and distortion (SINAD)
Lectures 15-16: TF Testing
Copyright 2008, Agrawal
28

Problem for Solution

Show that for a nonlinear device with a single frequency input of amplitude A , the n th harmonic component in the output always contains a term proportional to A n .
29 Copyright 2008, Agrawal
Lectures 15-16: TF Testing


THD is the total power contained in all harmonics of a signal expressed as percentage (or ratio) of the fundamental signal power.

THD(%) = [(P
2
+ P
3

Or THD(%) = [(V
2
2

Where P
2
, P
3
+ · · · ) / P fundamental
+ V
3
2 + · · · ) / V 2
] × 100% fundamental
] × 100%
, . . . , are the power in watts of second, third, . . . , harmonics, respectively, and P fundamental power, is the fundamental signal

And V
2
, V
3
, . . . , are voltage amplitudes of second, third, . . . , harmonics, respectively, and V fundamental is the fundamental signal amplitude.

Also, THD(dB) = 10 log THD(%)

For an ideal distortionless signal, THD = 0% or – ∞ dB
30
Copyright 2008, Agrawal
Lectures 15-16: TF Testing


THD is specified typically for devices with RF output.

Separate power measurements are made for the fundamental and each harmonic.

THD is tested at specified power level because

THD may be small at low power levels.

Harmonics appear when the output power of an RF device is raised.
Copyright 2008, Agrawal 31
Lectures 15-16: TF Testing


The harmonics produced due to nonlinearity in an amplifier reduce the fundamental frequency power output (and gain). This is known as gain compression .

As input power increases, so does nonlinearity causing greater gain compression.
 A standard measure of Gain compression is “1-dB compression point” power level P
1dB
, which can be

Input referred for receiver, or

Output referred for transmitter
Copyright 2008, Agrawal 32
Lectures 15-16: TF Testing

f
1
Copyright 2008, Agrawal
time time
LNA or PA frequency
Lectures 15-16: TF Testing f
1 frequency
33

time
LNA or PA time f
1
Copyright 2008, Agrawal frequency
Lectures 15-16: TF Testing f
1 f
2 f
3 frequency
34


Assume a transfer function, v o
= a
0
+ a
1 v i
+ a
3
+ a
2 v i
2 v i
3

Let v i
= A cos ωt

Using the identities ( ω = 2πf):
 cos 2 ωt = (1 + cos 2ωt)/2
 cos 3 ωt = (3 cos ωt + cos 3ωt)/4

We get,
 v o
= a
0
+ a
2
A 2 /2 + (a
1
A + 3a
3
A 3 /4) cos ωt
+ (a
2
A 2 /2) cos 2 ωt + (a
3
A 3 /4) cos 3 ωt
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
35


DC term is filtered out.

For small-signal input, A is small

A 2 and A 3 terms are neglected
 v o
= a
1
A cos ωt, small-signal gain, G
0
= a
1

Gain at 1-dB compression point, G
1dB
= G
0
– 1

Input referred and output referred 1-dB power:
P
1dB(output)
– P
1dB(input)
= G
1dB
= G
0
– 1
Lectures 15-16: TF Testing

Copyright 2008, Agrawal
1 dB
1 dB
Compression point
Linear region
(small-signal)
Compression region
P
1dB(input)
Input power (dBm)
Lectures 15-16: TF Testing
37


Apply a single-tone input signal:
1.
Measure the gain at a power level where DUT is linear.
2.
Extrapolate the linear behavior to higher power levels.
3.
Increase input power in steps, measure the gain and compare to extrapolated values.
4.
Test is complete when the gain difference between steps 2 and 3 is 1dB.

Alternative test: After step 2, conduct a binary search for 1-dB compression point.
38
Copyright 2008, Agrawal
Lectures 15-16: TF Testing


Small-signal gain, G
0
= 28dB

Input-referred 1-dB compression point power level,
P
1dB(input)

We compute:
= – 19 dBm

1-dB compression point Gain, G
1dB
= 28 – 1 = 27 dB

Output-referred 1-dB compression point power level,
P
1dB(output)
=
=
P
1dB(input)
– 19 + 27
+ G
1dB
= 8 dBm
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
39


Intermodulation distortion is relevant to devices that handle multiple frequencies.

Consider an input signal with two frequencies ω
1 and ω
2
: v i
= A cos ω
1 t + B cos ω
2 t

Nonlinearity in the device function is represented by v o
= a
0
+ a
1 v i
+ a
2 v i
2 + a
3

Therefore, device output is v i
3 , neglecting higher order terms v o
= a
0
+ a
+ a
+ a
1
2
3
(A cos ω
1 t + B cos ω
2 t) DC and fundamental
(A cos ω
1 t + B cos ω
2 t) 2
(A cos ω
1 t + B cos ω
2 t) 3
2
3 nd rd order terms order terms
40
Copyright 2008, Agrawal
Lectures 15-16: TF Testing

Problems to Solve

Derive the following: v o
= a
0
+ a
1
(A cos ω
1 t + B cos ω
2 t)
+ a
2
[ A 2 (1+cos 2
+ AB cos ( ω
ω
1 t)/2 + AB cos ( ω
1
– ω
2
)t + B 2 (1+cos 2 ω
1
+ ω
2 t)/2 ]
2
)t
+ a
3
(A cos ω
1 t + B cos ω
2 t) 3

Hint: Use the identity:
 cos α cos β = [cos(α + β) + cos(α – β)] / 2

Simplify a
3
(A cos ω
1 t + B cos ω
2 t) 3
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
41


Order for distortion product mf
1
± nf
2 is |m| + |n|
Nunber of distortion products Frequencies
Order Harmonic Intermod.
Total Harmonic
2
3
4
5
6
7
N
2
2
2
2
2
2
2 2N
2
4
6
8
10
12
– 2
4
6
8
10
12
14
2N
2f
3f
4f
5f
6f
7f
Nf
1
1
1
1
1
1
1
, 2f
, 3f
, 4f
, 5f
, 6f
, 7f
, Nf
2
2
2
2
2
2
2
Intrmodulation f
1
+ f
2
, f
2
– f
1
2f
1
± f
2
, 2f
2
± f
1
2f
1
3f
1
± 2f
± f
2
2
, 2f
, 3f
2
2
– 2f
± f
1
1
,
3f
1
4f
1
± 2f
± f
2
2
, 3f
, 4f
2
2
± 2f
± f
1
1
,
3f
1
5f
2
± 3f
± f
1
2
, 3f
, 4f
1
2
– 3f
± 2f
2
1
, 5f
1
, 4f
2
± f
± 2f
1
2
,
4f
1
5f
2
± 3f
± 2f
1
2
, 4f
2
, 6f
1
– 3f
1
, 5f
1
± f
2
, 6f
2
± 2f
± f
1
2
,
. . . . .
42
Copyright 2008, Agrawal
Lectures 15-16: TF Testing

Problem to Solve
Write Distortion products tones 100MHz and 101MHz
Order
Harmonics
(MHz)
Intermodulation products (MHz)
4
5
2
3
200, 202
300, 303
400, 404
500, 505
1, 201
99, 102 , 301, 302
2, 199, 203, 401, 402, 403
98 , 103 , 299, 304, 501, 503, 504
6 600, 606
3, 198, 204, 399, 400, 405, 601, 603, 604,
605
7 700, 707
97 , 104 , 298, 305, 499, 506, 701, 707,
703, 704, 705, 706
Intermodulation products close to input tones are shown in bold.
43
Copyright 2008, Agrawal
Lectures 15-16: TF Testing

f
1 f
2 frequency
DUT
Copyright 2008, Agrawal
Lectures 15-16: TF Testing f
1 f
2
2f
1 frequency
2f
2
44

DUT Third-order intermodulation distortion products (IMD3) f
1 f
2 frequency
Copyright 2008, Agrawal f
1 f
2
2f
1
2f
2 frequency
3f
1
3f
2
Lectures 15-16: TF Testing
45

Problem to Solve

For A = B, i.e., for two input tones of equal magnitudes, show that:

Output amplitude of each fundamental frequency, f
1 or f
2
, is a
1
9
A + — a
3
4
A 3 ≈ a
1
A

Output amplitude of each third-order intermodulation frequency, 2f
1
– f
2 or 2f
2
– f
1
, is
3
— a
3
4
A 3
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
46


IP3 is the power level of the fundamental for which the output of each fundamental frequency equals the output of the closest third-order intermodulation frequency.

IP3 is a figure of merit that quantifies the third-order intermodulation distortion.

Assuming a
1
>> 9a
3
A 2 /4, IP3 is given by a
1
IP3 = 3a
3
IP3 3 / 4
IP3 = [4a
1
/(3a
3
)] 1/2 a
1
A
3a
3
A 3 / 4
IP3
A
47 Copyright 2008, Agrawal
Lectures 15-16: TF Testing


Select two test frequencies, f
1 magnitude to the input of DUT.
and f
2
, applied in equal

Increase input power P
0
(dBm) until the third-order products are well above the noise floor.

Measure output power P
1 frequency and P
3 frquency.
in dBm at any fundamental in dBm at a third-order intermodulation

Output-referenced IP3: OIP3 = P
1

Input-referenced IP3: IIP3 = P
0
+ (P
1
+ (P
1
– P
3
) / 2
– P
3
) / 2
= OIP3 – G
Because, Gain for fundamental frequency, G = P
1
– P
0
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Lectures 15-16: TF Testing
48

Copyright 2008, Agrawal
OIP3
P
1 f
1 or f
2
20 log a
1 slope = 1
A
P
3
P
0
IIP3
Input power = 20 log A dBm
Lectures 15-16: TF Testing
2f
1
– f
2 or 2f
2
20 log (3a
3
– f
1
A 3 /4) slope = 3
(P
1
– P
3
)/2
49


Gain of LNA = 20 dB

RF signal frequencies: 2140.10MHz and 2140.30MHz

Second-order intermodulation distortion: 400MHz; outside operational band of LNA.

Third-order intermodulation distortion: 2140.50MHz; within the operational band of LNA.

Test:

Input power, P
0
= – 30 dBm, for each fundamental frequency

Output power, P
1
= – 30 + 20 = – 10 dBm

Measured third-order intermodulation distortion power, P
3

OIP3 = – 10 + [( – 10 – ( – 84))] / 2 = + 27 dBm
= – 84 dBm

IIP3 = – 10 + [( – 10 – ( – 84))] / 2 – 20 = + 7 dBm
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Lectures 15-16: TF Testing
50


Noise in an RF system is unwanted random fluctuations in a desired signal.

Noise is a natural phenomenon and is always present in the environment.

Effects of noise:

Interferes with detection of signal (hides the signal).

Causes errors in information transmission by changing signal.

Sometimes noise might imitate a signal falsely.

All communications system design and operation must account for noise.
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Lectures 15-16: TF Testing
51


Consider noise as a random voltage or current function, x(t), over interval – T/2 < t < T/2.

Fourier transform of x(t) is X
T
(f).

Power spectral density (PSD) of noise is power across 1 Ω
S x
(f) = lim [ E{ |X
T
(f)| 2 } / (2T) ] volts 2 /Hz
T→∞
This is also expressed in dBm/Hz.
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52


Thermal (Johnson) noise: Caused by random movement of electrons due to thermal energy that is proportional to temperature.

Called white noise due to uniform PSD over all frequencies.

Mean square open circuit noise voltage across R Ω resistor [Nyquist, 1928]: v 2 = 4hfBR / [exp(hf/kT) – 1]

Where
 Plank’s constant h = 6.626 × 10 34 J-sec

Frequency and bandwidth in hertz = f, B
 Boltzmann’s constant k = 1.38 × 10 – 23 J/K

Absolute temperature in Kelvin = T
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Lectures 15-16: TF Testing
53

Problem to Solve

Given that for microwave frequencies, hf << kT, derive the following Rayleigh-Jeans approximation: v 2 = 4kTBR

Show that at room temperature (T = 290K), thermal noise power supplied by resistor R to a matched load is ktB or
– 174 dBm/Hz.
Noisy resistor
R
R
Matched load v = (4kTBR) 1/2
Copyright 2008, Agrawal Lectures 15-16: TF Testing 54


Shot noise [Schottky, 1928]: Broadband noise due to random behavior of charge carriers in semiconductor devices.

Flicker (1/f) noise: Low-frequency noise in semiconductor devices, perhaps due to material defects; power spectrum falls off as 1/f. Can be significant at audio frequencies.

Quantization noise: Caused by conversion of continuous valued analog signal to discrete-valued digital signal; minimized by using more digital bits.

Quantum noise: Broadband noise caused by the quantized nature of charge carriers; significant at very low temperatures (~0K) or very high bandwidth ( > 10 15 Hz).

Plasma noise: Caused by random motion of charges in ionized medium, possibly resulting from sparking in electrical contacts; generally, not a concern.
Lectures 15-16: TF Testing


Expressed as noise power density in the units of dBm/Hz.

Noise sources:

Resistor at constant temperature, noise power = kTB W/Hz.

Avalanche diode

Noise temperature:

T n
= (Available noise power in watts)/(kB) kelvins

Excess noise ratio (ENR) is the difference in the noise output between hot (on) and cold (off) states, normalized to reference thermal noise at room temperature (290K):

ENR = [k( T h
– T c
)B]/(kT
0
B) = ( T h
/ T
0
) – 1

Where noise output in cold state is takes same as reference.

10 log ENR ~ 15 to 20 dB
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Lectures 15-16: TF Testing


SNR is the ratio of signal power to noise power.
S i
/N i
G S o
/N o
Input signal: low peak power, good SNR
Output signal: high peak power, poor SNR
G
S o
/N o
S i
/N i
Noise floor
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Frequency (Hz)
Lectures 15-16: TF Testing
57


Noise factor (F) is the ratio of input SNR to output SNR:

F = (S i
/N i
) / (S o
/N o
)
= N o
/ ( GN i
), when S i
= 1W and G = gain of DUT
= N o
 F ≥ 1
/( kT
0
BG), when N i
= kT
0
B for input noise source

Noise figure (NF) is noise factor expressed in dB:

NF = 10 log F dB
 0 ≤ NF ≤ ∞
58
Copyright 2008, Agrawal
Lectures 15-16: TF Testing


Friis equation [Proc. IRE, July 1944, pp. 419 – 422]:
F sys
= F
1
F
2
– 1 F
3
– 1 F n
– 1
+ ——— + ——— + · · · · + ———————
G
1
G
1
G
2
G
1
G
2
· · · G n – 1
Gain = G
1
Noise factor
= F
1
Gain = G
2
Noise factor
= F
2
Gain = G
3
Noise factor
= F
3
Gain = G n
Noise factor
= F n
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Lectures 15-16: TF Testing
59


Example: SOC receiver with large gain so noise output is measurable; noise power should be above noise floor of measuring equipment.

Gain G is known or previously measured.

Noise factor, F = N o
/ (kT
0

N o
BG), where is measured output noise power (noise floor)

B is measurement bandwidth

At 290K, kT
0
= – 174 dBm/Hz

Noise figure, NF = 10 log F
= N o
(dB) – ( – 174 dBm/Hz) – B(dB) – G(dB)

This measurement is also done using S-parameters.
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Lectures 15-16: TF Testing
60


Y – factor is the ratio of output noise in hot (power on) state to that in cold (power off) state.

Y = N h
/ N c
= N h
/ N
0

Y is a simple ratio.

Consider, N h
= kT h
BG and N c
= kT
0
BG

Then N h
– N c
= kBG( T h
– T
0
) or kBG = ( N h
– N c
) / ( T h
– T
0
)

Noise factor, F = N h
/( kT
0
BG) = ( N h
/ T
0
) [ 1 / (kBG) ]
= ( N h
/ T
0
) ( T h
– T
0
) / (N h
– N c
)
= ENR / (Y – 1)
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Lectures 15-16: TF Testing
61


Noise source provides hot and cold noise power levels and is characterized by ENR (excess noise ratio).

Tester measures noise power, is characterized by its noise factor F
2 and Y-factor Y
2
.

Device under test (DUT) has gain G
1

Two-step measurement: and noise factor F
1
.

Calibration: Connect noise source to tester, measure output power for hot and cold noise inputs, compute Y
2 and F
2
.

Measurement: Connect noise source to DUT and tester cascade, measure output power for hot and cold noise inputs, compute compute Y
12
, F
12 and G
1

Use Friis equation to obtain F
1
.
.
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Lectures 15-16: TF Testing
62

Noise source
ENR
Tester
(power meter)
F
2
, Y
2

Y
2

F
2
= N h2

N h2
/ N c2
, where
= measured power for hot source

N c2
= measured power for cold source
= ENR / (Y
2
– 1)
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
63

Noise source
ENR
DUT
F
1
, Y
1
, G
1
Tester
(power meter)
F
2
, Y
2
F
12
, Y
12

Y
12
= N h12

N h12
/ N c12
, where
= measured power for hot source

N c12
= measured power for cold source

F
12

G
1
= ENR / ( Y
12
= ( N h12
– N c12
– 1 )
) / ( N h2
– N c2
)
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
64

Problem to Solve

Show that from noise measurements on a cascaded system, the noise factor of DUT is given by
F
1
= F
12
F
2
– 1
– ———
G
1
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
65


Phase noise is due to small random variations in the phase of an
RF signal. In time domain, phase noise is referred to as jitter .

Understanding phase:
δ amplitude noise t
V sin ωt t
φ phase noise
[V + δ(t)] sin [ωt + φ(t)]
ω
Frequency (rad/s)
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Lectures 15-16: TF Testing
ω
Frequency (rad/s)
66


Similar to phase modulation by a random signal.

Two types:

Long term phase variation is called frequency drift .

Sh ort term phase variation is phase noise .

Definition: Phase noise is the Fourier spectrum (power spectral density) of a sinusoidal carrier signal with respect to the carrier power.
L(f) = P n
= P n
/P c
(as ratio) in dBm/Hz – P c in dBm (as dBc)

P n

P c is RMS noise power in 1-Hz bandwidth at frequency f is RMS power of the carrier
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Lectures 15-16: TF Testing
67

[V + δ(t)] sin [ωt + φ(t)] = [V + δ(t)] [sin ωt cos φ(t) + cos ωt sin φ(t)]
≈ [V + δ(t)] sin ωt + [V + δ(t)] φ(t) cos ωt
In-phase carrier frequency with amplitude noise
White noise δ(t) corresponds to noise floor
Quadrature-phase carrier frequency with amplitude and phase noise
Short-term phase noise corresponds to phase noise spectrum
Phase spectrum, L(f) = S
φ
Where S
φ
(f)/2
(f) is power spectrum of φ(t)
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Lectures 15-16: TF Testing
68


Phase noise is measured by low noise receiver
(amplifier) and spectrum analyzer:

Receiver must have a lower noise floor than the signal noise floor.

Local oscillator in the receiver must have lower phase noise than that of the signal.
Signal spectrum
Receiver phase noise
Receiver noise floor
Frequency (Hz)
Lectures 15-16: TF Testing Copyright 2008, Agrawal
69

Pure tone
Input
(carrier)
DUT
Spectrum analyzer power measurement
Power (dBm) over resolution bandwith (RBW)
Copyright 2008, Agrawal
Lectures 15-16: TF Testing offset carrier
Hz
70


Spectrum analyzer data:

RBW = 100Hz


Frequency offset = 2kHz

P carrier

P offset
= – 5.30 dBm
= – 73.16 dBm
Phase noise, L(f) = P offset
– P carrier
– 10 log RBW
= – 73.16 – ( – 5.30) – 10 log 100
= – 87.86 dBc/Hz
 Phase noise is specified as “ – 87.86 dBc/Hz at 2kHz from the carrier.”
Copyright 2008, Agrawal
Lectures 15-16: TF Testing
71

Problem to Solve

Consider the following spectrum analyzer data:

RBW = 10Hz

Frequency offset = 2kHz

P carrier

P offset
= – 3.31 dBm
= – 81.17 dBm

Determine phase noise in dBc/Hz at 2kHz from the carrier.
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Lectures 15-16: TF Testing
72

1.
S. Bhattacharya and A. Chatterjee, "RF Testing," Chapter 16, pages
745-789, in System on Chip Test Arch itectures, edited by L.-T. Wang,
C. E. Stroud and N. A. Touba, Amsterdam: Morgan-Kaufman, 2008.
2.
M. L. Bushnell and V. D. Agrawal, Essentials of Electronic Testing for
Digital, Memory & Mixed-Signal VLSI Circuits , Boston: Springer, 2000.
3.
J. Kelly and M. Engelhardt, Advanced Production Testing of RF, SoC, and SiP Devices , Boston: Artech House, 2007.
4.
B. Razavi, RF Microelectronics , Upper Saddle River, New Jersey:
Prentice Hall PTR, 1998.
5.
J. Rogers, C. Plett and F. Dai, Integrated Circuit Design for High-Speed
Frequency Synthesis , Boston: Artech House, 2006.
6.
K. B. Schaub and J. Kelly, Production Testing of RF and System-on-a-
Chip Devices for Wireless Communications , Boston: Artech House,
2004.
Copyright 2008, Agrawal Lectures 15-16: TF Testing
73