Transcript Intermodulation and the 3rd Order Intercept Point
Receiver Metrics:
Theory and Practice Intermodulation and the 3
rd
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 2
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 3
Questions on the Table
What is intermodulation distortion?
What is the 3
rd
order intercept point?
What do these characteristics mean in practice?
Intermodulation and the 3rd Order Intercept Point: Theory and Practice 4
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 5
Gain and the Compression Point
CP
Input Intermodulation and the 3rd Order Intercept Point: Theory and Practice At low input levels, receiver RF and IF stage gain will be generally linear— approaching a level called the
small signal asymptotic value.
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 ( or 3 dB below the small-signal asymptotic value.
CP
is frequently given as either 1 dB ). The compression point, stated in dB, 6
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 7
Intermodulation Distortion Products: An Example
(1) Fifth-Order (2) Third-Order
(3) Signal One (4) Signal Two
(5) Third-Order (6) Fifth-Order Intermodulation and the 3rd Order Intercept Point: Theory and Practice 3f1-2f2 2f1-f2
f1 f2
2f2-f1 3f2-2f1 7.218
7.221
7.224
7.227
7.230
7.233
8
Intermodulation Distortion Products: An Example
(1) Fifth-Order (2) Third-Order
(3) Signal One (4) Signal Two
(5) Third-Order (6) Fifth-Order Intermodulation and the 3rd Order Intercept Point: Theory and Practice 3f1-2f2 2f1-f2
f1 f2
2f2-f1 3f2-2f1 7.218
7.221
7.224
7.227
7.230
7.233
9
Intermodulation Distortion Products: An Example
(1) Fifth-Order (2) Third-Order
(3) Signal One (4) Signal Two
(5) Third-Order (6) Fifth-Order Intermodulation and the 3rd Order Intercept Point: Theory and Practice 3f1-2f2 2f1-f2
f1 f2
2f2-f1 3f2-2f1 7.218
7.221
7.224
7.227
7.230
7.233
10
Intermodulation Distortion Products: An Example
120 100 80
f 1 f 2
60 40
3f 1 - 2f 2
20
2f 1 - f 2 2f 2 - f 1 3f 2 - 2f 1
0 7.216
7.218
7.220
7.222
7.224
7.226
7.228
7.230
7.232
7.234
Intermodulation and the 3rd Order Intercept Point: Theory and Practice 11
Why it is called 3
rd
order
V
The performance of an ideal amplifier can be represented by the transfer function:
out
A
0
A
1
V in
An amplifier with some distortion due to
nonlinearities
power series expansion: can be expressed by a transfer function in the form of a
V out
A
0
A
1
V in
A
2
V in
2
A
3
V in
3
A
4
V in
4 ....
An input signal with two frequencies 1 and 2 may be shown as:
V in
V
1 cos( 1
t
)
V
2 cos( 2
t
) The
first
order term
A
0
A
1
V in
gives the fundamental products
V out
A
0
A
1
V
1 cos( 1
t
)
A
1
V
2 cos( 2
t
) The
second
order term
A
2
V in
2 determines the second order products:
A
2
V in
2
A
2
V
1 2 2
A
2
V
2 2 2
A
2
V
1 2 cos( 2 1
t
) 2
A
2
V
2 2 cos( 2 2
t
) 2
A
2
V
1
V
2 [cos( 1
t
2 2
t
) cos( 1
t
2
t
)]
DC terms 2 nd harmonic terms 2 nd order IMD terms
Intermodulation and the 3rd Order Intercept Point: Theory and Practice 12
Why it is called 3
rd
order
(cont’d) The
third
order term
A
3
V in
3 determines the third order products:
A
3
V in
3 3
A
3 2
V
1
V
2 2
V
1 3 2 cos( 1
t
) 3
A
3 2 cos
V
1 2
V
2
V
2 3 2 cos( 2
t
)
Fundamental frequency terms
A
3
V
1 3 cos( 3 1
t
) 4
A
3
V
2 3 cos( 3 2
t
) 4
3 rd harmonic terms
3
A
3
V
1 2
V
2 [cos( 2 1
t
2
t
) cos( 2 1
t
2
t
)] 4 3
A
3
V
1
V
2 2 [cos( 2 2
t
4 1
t
) cos( 2 2
t
1
t
)]
3 rd order IMD terms – The troublemakers
Intermodulation and the 3rd Order Intercept Point: Theory and Practice 13
Third Order Intermodulation Products
The 3 rd order products will be the largest (loudest) of the intermodulation products.
As a general rule, the 3 receiver.
rd 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 Intermodulation and the 3rd Order Intercept Point: Theory and Practice 14
ARRL Receiver Test:
Measured Response of the Signal of Interest
Intermodulation and the 3rd Order Intercept Point: Theory and Practice 15
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 16
ARRL Receiver Test:
Measured Response of the IMD Product
Intermodulation and the 3rd Order Intercept Point: Theory and Practice 17
ARRL Receiver Test:
Extrapolated Linear Region of the Measured Response of the IMD Product
3 rd Order Intercept Point Intermodulation and the 3rd Order Intercept Point: Theory and Practice 18
The 3
rd
order intercept point (IP3): A Measure of Merit
Our graph illustrates that the 3 rd 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 3 rd 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 3 rd order intermodulation products. More on this later.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice 19
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 20
Compression-Free Dynamic Range
L b
Compression-Free Dynamic Range
U b L b
Lower bound The lower bound is Defined as a signal of interest 3 dB greater than the noise floor.
U b
Upper bound The upper bound is set by the compression point of the desired (on-channel) signal.
Intermodulation and the 3rd Order Intercept Point: Theory and Practice 21
Spurious-Free Dynamic Range
Spurious-Free Dynamic Range
L b U b L b
Lower bound The lower bound is defined as a signal of interest 3 dB greater than the noise floor.
U b
Upper bound The upper bound is set by the 3 MDS.
rd order IMD equal to the Intermodulation and the 3rd Order Intercept Point: Theory and Practice 22
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Intermodulation and the 3rd Order Intercept Point: Theory and Practice 23
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 signals f 1 and f 2 Lower bound greater than our signal of interest. An unlikely occurrence except in unique circumstance.
Spurious-Free Dynamic Range Defined as a signal of interest 3 dB greater than the noise floor.
L b U b U b
Upper bound The upper bound is set by the 3 MDS.
rd order IMD equal to the Intermodulation and the 3rd Order Intercept Point: Theory and Practice 24
Spurious-Free Dynamic Range
Intermodulation and the 3rd Order Intercept Point: Theory and Practice 25
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 26
From ARRL test reports in QST magazine (at 14 MHz w preamp off)
Example performance data
Model ICOM IC-9500 Receiver Elecraft K3/10 IMD Dynamic Range 20 kHz spacing (dB) 103 IP3 20 kHz spacing (dBm) +31 IMD Dynamic Range 5 kHz spacing (dB) 102 99 +12 102 IP3 5 kHz spacing (dBm) +14 +23 Ten-Tec Orion II 92 Yaesu FT 1000MP Mark V ICOM IC-7800 97.5
108 +20 +20.3
+20 96 72.5
96 +20 -5.2
+27 Intermodulation and the 3rd Order Intercept Point: Theory and Practice 27
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 3 rd 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 29
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 30
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 3 rd 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
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References
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. 15.18 15.21
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 33
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 35