Receiver Metrics:
Theory and Practice
Intermodulation and
the 3rd Order Intercept Point
Carl Ferguson, W4UOA
John Drum, W4BXI
John Krupsky, WA5MLF
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Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Example Receiver Types & Specs

A DC to 30 GHz broadband amplifier using AlGaAs-GaAs
heterojunction bipolar transistor (HBT) technology.
7.8 dB gain, IP3=23.9 dBm
(ref IEEE Microwave and Guided Wave Letters, Aug 1991)

Monolithic SPDT X-band PIN diode switch. Insertion loss of
0.89 dB, off-isolation >35 dB at 10 GHz, IP3=29.6 dBm.
(ref IEEE Microwave and Guided Wave Letters, Oct 1993)


A 44-GHz monolithic microwave integrated circuit (MMIC)
amplifier based on InP HBT technology. Gain as high as 7.6 dB,
peak IP3=34 dBm. (ref IEEE Journal of Solid-State Circuits, Sep 1999)
PIN photodetectors for RF optical fiber links. Measurement of
IP3=27 dBm using a four laser heterodyne system.
(ref IEEE Photonics Technology Letters, Apr 2000)
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Questions on the Table
 What is intermodulation distortion?
 What is the 3rd order intercept point?
 What do these characteristics mean in
practice?
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Linear Gain
Linear gain in a circuit is
normally represented by a
straight line.
The scale on the Input and
Output axis reflect the gain
through the circuit. In this
example, a gain of 2:1.
However, all RF & IF
circuits are inherently
nonlinear.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Gain and the
Compression Point
Output
At low input levels, receiver RF and IF
stage gain will be generally linear—
approaching a level called the smallsignal asymptotic value.
CP
But as the input level increases, gain
through the stage becomes
increasingly nonlinear. When the gain
falls n dB below the small-signal
asymptotic value, it has said to have
reached its compression point (CP).
The compression point, stated in dB,
is frequently given as either 1 dB
or 3 dB below the small-signal
asymptotic value.
Input
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Nonlinearity and
Intermodulation Distortion
 Nonlinearity in RF and IF circuits leads to two
undesirable outcomes: harmonics and intermodulation
distortion.
 Harmonics in and of themselves are not particularly
troublesome.
 For example, if we are listening to a QSO on
7.230 MHz, the second harmonic, 14.460 MHz is well
outside the RF passband.
 However, when the harmonics mix with each other
and other signals in the circuit, undesirable and
troublesome intermodulation products can occur.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Intermodulation Distortion
Products: An Example
(1)
Fifth-Order
3f1-2f2
7.218
(2)
Third-Order
2f1-f2
7.221
(3)
Signal One
f1
7.224
(4)
Signal Two
f2
7.227
(5)
Third-Order
2f2-f1
7.230
(6)
Fifth-Order
3f2-2f1
7.233
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Intermodulation Distortion
Products: An Example
(1)
Fifth-Order
3f1-2f2
7.218
(2)
Third-Order
2f1-f2
7.221
(3)
Signal One
f1
7.224
(4)
Signal Two
f2
7.227
(5)
Third-Order
2f2-f1
7.230
(6)
Fifth-Order
3f2-2f1
7.233
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Intermodulation Distortion
Products: An Example
(1)
Fifth-Order
3f1-2f2
7.218
(2)
Third-Order
2f1-f2
7.221
(3)
Signal One
f1
7.224
(4)
Signal Two
f2
7.227
(5)
Third-Order
2f2-f1
7.230
(6)
Fifth-Order
3f2-2f1
7.233
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Intermodulation Distortion
Products: An Example
120
f1
f2
100
dB
80
60
40
2f1- f2
2f2- f1
3f2- 2f1
3f1- 2f2
20
0
7.216
7.218
7.220
7.222
7.224
7.226
7.228
7.230
7.232
7.234
mHz
MHz
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Why it is called 3rd order
The performance of an ideal amplifier can be represented by the transfer function:
Vout  A0  A1Vin
An amplifier with some distortion due to nonlinearities can be expressed by a transfer function in the form of a
power series expansion:
Vout  A0  A1Vin  A2Vin  A3Vin  A4Vin
2
3
4
....
Vin  V1 cos(1t )  V2 cos(2t )
An input signal with two frequencies 1 and 2 may be shown as:
The first order term
A0  A1Vin
The second order term
A2Vin
2
gives the fundamental products
Vout  A0  A1V1 cos(1t )  A1V2 cos(2t )
determines the second order products:
A2V12 A2V22 A2V12
A2V22
A VV
AV 


cos( 21t ) 
cos( 22t )  2 1 2 [cos(1t  2t )  cos(1t  2t )]
2
2
2
2
2
2
2 in
DC terms
2nd harmonic terms
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
2nd order IMD terms
12
Why it is called 3rd order
The third order term
A3Vin
3
(cont’d)
determines the third order products:
 2
V23 
3 A3  2 V13 
3 A3
AV 
V1V2   cos(1t ) 
cos V1 V2   cos(2t ) 
2 
2
2
2

3
3 in
A3V13
A3V23
cos(31t ) 
cos(32t ) 
4
4
Fundamental frequency terms
3rd harmonic terms
3 A3V12V2
3 A3V1 V22
[cos( 21t  2t )  cos( 21t  2t )] 
[cos( 22t  1t )  cos( 22t  1t )]
4
4
3rd order IMD terms – The troublemakers
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Third Order
Intermodulation Products
 The 3rd order products will be the largest
(loudest) of the intermodulation products.
 As a general rule, the 3rd order products
will increase (grow) 3-times faster than the
fundamental signal (the signal of interest).
However, recent lab studies have revealed
that this relation can vary from receiver to
receiver.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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ARRL Receiver Test:
Measured Response of the Signal of Interest
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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ARRL Receiver Test:
Extrapolated Linear Region of the
Measured Response of the Signal of Interest
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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ARRL Receiver Test:
Measured Response of the IMD Product
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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ARRL Receiver Test:
Extrapolated Linear Region of the
Measured Response of the IMD Product
3rd Order Intercept Point
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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The 3rd order intercept point (IP3):
A Measure of Merit
Our graph illustrates that the
3rd order intercept point is
defined by the intersection of
two hypothetical lines. Each
line is an extension of a linear
gain figure: first of the signal
of interest; and second, of
the 3rd order intermodulation
distortion product—from which
IP3 gets its name.
You will note that the larger the value of IP3, the less likely the
receiver will be adversely affected by 3rd order intermodulation
products. More on this later.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Dynamic Range:
A Measure of Merit

The ratio of the smallest usable signal to the largest
tolerable signal.

The amplitude range over which a mixer can operate
without degradation of performance.

Noise should determine the lower limit of a receiver’s
dynamic range.

The lower limit may be defined by the signal-to-noise ratio
of a desired signal at its output. This measure is generally
favored because of its empirical nature—it can be easily
calculated.

However, the lower limit can be set by the MDS—a some
what more qualitative measure.

The upper limit is normally set by either noise or distortion.
Source: QEX, July/August, 2002.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Compression-Free Dynamic Range
Lb
Compression-Free
Dynamic Range
Lb
The lower bound is
Defined as a signal
of interest 3 dB
greater than the
noise floor.
Ub
Ub
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
Lower bound
Upper bound
The upper bound is
set by the compression
point of the desired
(on-channel) signal.
21
Spurious-Free Dynamic Range
Lb
The lower bound is
defined as a signal
of interest 3 dB
greater than the
noise floor.
Spurious-Free
Dynamic Range
Lb
Ub
Ub
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
Lower bound
Upper bound
The upper bound is
set by the 3rd order
IMD equal to the
MDS.
22
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Intermodulation and the 3rd Order Intercept Point: Theory and Practice
23
Why is it important to have a wide dynamic range?
Spurious-Free Dynamic Range
Notice below that an input signal of -110 dBm will produce
20 dB output in our signal of interest. To achieve 20 dB
output in the third order product, the off channel test
Lower
signals f1 and f2 must be 80 dB (110 dBm –Lb30
dBm)bound
greater than our signal of interest. An unlikely
occurrence
The lower
bound is
except in unique circumstance.
Defined as a signal
of interest 3 dB
greater than the
noise floor.
Spurious-Free
Dynamic Range
Lb
Ub
Ub
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
Upper bound
The upper bound is
set by the 3rd order
IMD equal to the
MDS.
24
Spurious-Free Dynamic Range
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Spurious-Free Dynamic Range
FT-1000 IPO Button
Normally, the front-end FET RF
amplifiers provide maximum
sensitivity for weak signals. During
typical conditions on lower
frequencies (such as strong
overloading from signals on adjacent
frequencies), the RF amplifiers can
be bypassed by pressing the [IPO]
button so the green LED is on.
This improves the dynamic range and IMD (intermodulation distortion)
characteristics of the receiver, at a slight reduction of sensitivity. On
frequencies below about 10 MHz, you generally will want to keep the [IPO]
button engaged, as the preamplifiers are usually not needed at these
frequencies.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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From ARRL test reports in QST magazine
(at 14 MHz w preamp off)
Example performance data
Model
IMD Dynamic
Range 20 kHz
spacing (dB)
IP3
20 kHz spacing
(dBm)
IMD Dynamic
Range 5 kHz
spacing (dB)
IP3
5 kHz spacing
(dBm)
ICOM IC-9500
Receiver
103
+31
102
+14
Elecraft K3/10
99
+12
102
+23
Ten-Tec Orion II
92
+20
96
+20
Yaesu FT1000MP Mark V
97.5
+20.3
72.5
-5.2
ICOM IC-7800
108
+20
96
+27
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Automated IP3 Testing




An approach for built-in self testing of RF Integrated Circuits
was reported by the Department of Electrical and Computer
Engineering at Auburn University.
The goal is to reduce the cost of RF testing on manufactured
RFICs (operating in the 2-5 GHz range). The design would
provide the ability “to detect faults and to assist in
characterization and calibration during manufacturing and field
testing”.
The proposed design makes use of Direct Digital Synthesis
(DDS) test pattern generator and analyzer circuitry on the chip
to perform a 2-tone test and analyze the results.
The prototype design was found to provide accurate results for
IP3 values below 30 dBm and is thought to underestimate IP3
values above that.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
28
A Few Final Comments:
Sensitivity and Blocking
 While a receiver’s ability to handle 3rd order
intermodulation products is important—its sensitivity
and ability to handle strong adjacent signals is of
equal and maybe even greater importance.
 We obviously want our receiver to have a very low
noise figure—able to hear the weakest of signals. And,
we recognize that our RF and IF amplifiers can not
handle infinitely large signals—at some point the
amplifier will reach its compression point.
 What happens when large adjacent signals capture
the front-end of our receiver?
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Sensitivity and Blocking

Blocking happens when a large off channel signal causes
the front-end RF amplifier to be driven to its compression
point.

As a result all other signals are lost (blocked).

This condition is frequently called de-sensing—the
sensitivity of the receiver is reduced.

Blocking is generally specified as the level of the unwanted
signal at a given offset.

Original testing used a wide offset—typically 20 kHz. More
recently, recognizing our crowded band conditions and the
narrow spacing of CW and other digital modes, most testing
today is done with close spacing of 2 kHz.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Sensitivity and Blocking
 A good receiver design must find a balance between
sensitivity and strong signal handling capability. And
while the AGC in most receivers will attenuate large
signals, large off channel signals can dramatically
reduce a receiver’s sensitivity.
 For an excellent presentation on this subject, we refer
you to
http://www.sherwood-engineering.com
or
http://www.NC0B.com
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
31
Summary
 I hope we’ve answered a few of your
questions about:
 intermodulation distortion products;
 the 3rd order intercept point;
 dynamic range; and
 maybe stimulated your interest in learning
even more about receiver performance.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
32
References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
R. Sherwood, NC0B, “Roofing Filters, Transmitted IMD & Receiver Performance”, Presentation to Boulder,
Colorado Amateur Radio Club, February 2008, http://www.sherweng.com/
M. Tracy, KC1SX, “Changes to ARRL Receiver Tests”, QST, October 2007, pp. 70-71
J. Hallas, W1ZR, “Keeping the Lid on with a Roofing Filter”, QST, October 2007, pp. 57-58
D. Newkirk, AB2WH, “ICOM IC-9500 Communications Receiver”, Product Review, QST, January 2008, pp.69-73
B. Prior, N7RR, “First Look: Elecraft K3 HF/6 Meter Transceiver”, Product Review, QST, April 2008, pp. 41-45
D. Smith, KF6DX, “Improved Dynamic Range Testing”, QEX , Jul/Aug 2002, pp. 46-52
“Mixers, Modulators and Demodulators”, The ARRL Handbook for Radio Amateurs, 1998, Chapter 15 pp. 15.1815.21
U. Rohde, KA2WEU, “Testing and Calculating Intermodulation Distortion in Receivers”, QEX, July 1994, pp 3-4
K. Kundert, “Accurate and Rapid Measurement of IP2 and IP3”, The Designer’s Guide Community, May 2006,
http://www.designers-guide.org
S. Rumley, KI6QP, “A Precision Two-Tone RF Generator for IMD Measurements”, QEX, April 1995, pp. 6-12
“Radio receiver strong signal response”, Adrio Communications Ltd,
http://www.radio-electronics.com/info/receivers/overload/strong_signal_specs.php
M. Ellis, “Introduction to Mixers”, 1999, http://michaelgellis.tripod.com/mixersin.html
“High Dynamic Range Receiver Parameters”, Tech-notes, Vol.7, No. 2, Watkins-Johnson Company, March/April
1980
“Third Order Intercept Point Versus Sensitivity”, Application Note No. 1.01, Dynamic Sciences International,
Inc., May 2005, http://www.dynamicsciences.com/client/show_product/7
“Theory of Intermodulation Distortion Measurement”, Application Note 5C-043, Maury Microwave Corporation,
July 1999, http://www.maurymw.com/support/pdfs/5C-043.pdf
Foster Dai, et al., “Automatic Linearity (IP3) Test with Built-In Pattern Generator and Analyzer”, Proc. IEEE
International Test Conf., pp. 271-280, 2004, http://www.eng.auburn.edu/~strouce/class/bist/ITC04ip3.pdf
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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An early reference
Intercept point and undesired responses
Sagers, R.C.
Motorola, Inc., Fort Worth, Texas;
This paper appears in: Vehicular Technology Conference, 1982. 32nd IEEE
Publication Date: 23-26 May 1982
Volume: 32, On page(s): 219- 230
Posted online: 2006-06-19 10:22:27.0
Abstract
This paper presents a method for using the concept of intercept point to calculate the
undesired-response rejection ratio of a single stage. Single stages may be cascaded
together to form a system and the undesired response rejection ratio of the system
may be found using a procedure similar to cascaded noise figure. When applied to
receiver system design, this method allows easy calculation of such undesired
receiver responses as intermodulation distortion and spurious responses.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
34
A earlier reference
Two-Tone Nonlinearity Testing - The Intercept Point
Fulton, F.F.
This paper appears in: Microwave Symposium Digest, G-MTT International
Publication Date: Jun 1973
Volume: 73 ,
On page(s): 112 - 112
Posted online: 2003-01-06 17:17:01.0
Abstract
When a nonlinearity is modeled as memoryless with a three-term power series, a convenient way of
expressing the characteristics is by the use of intercept points. An intercept point is the output
power level at which the fundamental tone and the distortion tone have equal amplitudes. For many
practical system problems, specification of an intercept point permits very quick calculation of
distortion tone levels; in particular, given two equal amplitude fundamental tones at similar
frequencies, the adjacent third order distortion product is down from a fundamental by twice the
number of decibels that the fundamental is down from the third order intercept point. Even more
simply, the second order distortion is down from a fundamental by an amount equal to the number
of decibels that the fundamental is down from the appropriate intercept point.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice
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Thank you for your attention….