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INTERMODULATION DISTORTION (IMD)
By Christian Henn, Burr-Brown International, GmbH
gains and output voltage swings, group delay time, settling
time, rise time, slew rate, harmonic distortion, and IMD
performance. In the remaining sections the application note
describes the basics of intermodulation distortions, the relationship between fundamental and 3rd IMD, and shows the
test setup and test results for the OPA622 and OPA623.
The intermodulation distortion (IMD) performance of
wideband, DC-coupled amplifiers is a relatively new area
for integrated operational amplifier suppliers. New progresses
in IC technology extend the application of op amps where
some years ago discrete circuits played the major role.
Methods to measure and communicate the extent of this
distortion to users have been borrowed from traditional
“RF” companies which have historically supplied the radar
and radio communications industries, where the importance
of it was first highlighted.
HARMONIC DISTORTION
When Flash-A/D users talk about distortion they are generally concerned with the spurs introduced into the spectrum
of interest. In laboratory conditions harmonic distortion is a
major area of concern and is usually measured by inserting
a single-tone fundamental into the DUT, then looking at the
relevant frequency (2xf, 3xf) to determine the magnitude of
the harmonic tones. While this testing is useful to many
customers, it does not always appease everyone. Manufacturers who claim to have amplifiers with –3dB bandwidth in
the tens of MHz region often test distortion at relatively low
tones. While the results are undoubtedly favorable, the user
cannot use it for a circuit design. Harmonic distortion also
neglects the magnitude of spurs from other sources. Installed
in the equipment for which it was selected, there is no
guarantee that it will be exposed to a pure spectrum as it is
for harmonic distortion measurements. In many cases the
amplifier is asked to operate in spectrally-rich environments
where intermodulation distortion properties of the amp are
of keen interest.
Examples of applications demanding good intermodulation
distortion include:
• Radar
• Satellite Communications
• Digital Radio Receivers
• Nuclear Particle Research
• CAD Monitor Amplifier
In radar applications good IMD performance is essential,
because interference from other radars and jammers often
pollute the spectrum. For satellite communications systems,
the usable bandwidth for each transponder is limited and
multiple signals are frequency multiplicated onto one carrier
so that signals can interfere with each other when IMD
performance is low. For Digital Radio Receivers, a small
segment of a broader RF spectrum is digitized and scanned
by high-speed data signal processors. For CAD Monitor
Amplifiers and for Nuclear Particle Research test equipment, the IMD or as later described the intercept point
characterize more precisely than harmonic distortion the
large signal capabilities of wideband amplifiers.
MATHEMATICAL DERIVATION
OF INTERMODULATION DISTORTION
The usable dynamic range of an amplifier is limited at very
small signal levels by the noise floor and at large signal
levels by interferences between signal frequencies. Distortions are caused by non-linearities in the amplitude transfer
characteristics. As shown later for producing harmonics, the
transfer curve exists of a linear and a quadratic portion and
the typical output contains not only the fundamental frequency, but integer multiples of it. IMD results from the
mixing of two or more signals of different frequencies and
the transfer curve contains in addition a cubic portion. The
spurious output occurs at the sum and/or difference of
integer multiples of the input frequencies.
INTERMODULATION DISTORTION
IN THE OPA622 AND OPA623
The IMD test results in this application note center on new
ultra high-speed operational amplifiers available from BurrBrown—notably, the OPA622 voltage feedback amplifier
and the OPA623 current-feedback amplifier.
While the specifications are important and are fully tested,
the targeted market segments for these amplifiers clearly
called for superior AC performance. Enhanced testing for
these parts includes –3dB bandwidth curves for various
©
1994 Burr-Brown Corporation
SBOA077
AB-194
Printed in U.S.A. April, 1994
1
2
3
4
5
6
Remembering that [sin2x = (1 – cos2x)/2] and [sin(x)sin(y)
= (cos(x – y) – cos(x + y))/2] and substituting into
Equation 4 provides:
K 2 (V IN )2 = K 2 (E12 + E 22 ) / 2 −
(5a)
(K 2 / 2)(E12 cos 2ω1t + E 22 cos 2ω 2 t) +
(5b)
2K 2 E1E 2 (cos(ω1t − ω 2 t) − cos(ω1t + ω 2 t)) (5c)
I
The first and second terms in Equation 5 represent DC offset
and second-order harmonics. The third term is the secondorder IMD. This exercise can be repeated with the fourth
term of Equation 3 to study third-order effects.
K 3 (V IN )3 = K 3 (E13 sin 3 ω1t + E 32 sin 3 ω 2 t +
IA
BP
3E12 E 2 sin 2 ω1t(sin ω 2 t) +
Bias Point
3E1E 22 sin ω1t(sin 2 ω 2 t)
VK
Utilizing the identities, sin3x = 1/4(3sin – sin3x) and sin2xsiny
= 1/2(siny – 1/2(sin(2x + y) – sin(2x – y))), Equation 6
reduces to:
K 3 (V IN )3 =
VB
V
(3K 3 / 4)(E13 sin ω1t + E 32 sin ω 2 t +
FIGURE 1. Nonlinear Transfer Characteristics.
The non-ideal characteristics of an amplifier can be described by using the Power Series Expansion:
V OUT = K 0 + K1 (V IN ) + K 2 (V IN ) + K 3 (V IN ) + L (1)
2
3
A one-tone input signal (VΙΝ = Esinωt) produces harmonic
distortion, a two-tone input signal produces harmonic distortion and intermodulation distortion.
V IN = E1 sin ω1t + E 2 sin ω 2 t
(2)
Combining equations 1 and 2 results in the following identity:
V OUT = K 0 + K1 (E1 sin ω1t + E 2 sin ω 2 t)2 +
K 2 (E1 sin ω1t + E 2 sin ω 2 t)2 +
K 3 (E1 sin ω1t + E 2 sin ω 2 t)3 + L
(3)
The first term (K0) represents the DC offset of the amplifier,
the second term is the fundamental signal(s). The subsequent terms represent the distortion of the amplifier. The
second IMD can be found by analyzing the third term of
Equation 3.
2E12 E 2 sin ω 2 t + 2E 22 E1 sin ω1t)
(7a)
(K 3 E 32 / 4)(E13 sin 3ω1t + E 32 sin 3ω 2 t) +
(7b)
(3K 3 E12 E 2 / 2)(sin(2ω1t − ω 2 t) − 12 sin(2ω1t + ω 2 t)) +(7c)
(3K E 2 E / 2)(sin(2ω t − ω t) − 1 sin(2ω t + ω t)) (7d)
3
2 1
2
1
2
2
1
Term (a) from Equation 7 represents amplitude offset at the
fundamental frequencies. Term (b) signifies the third-order
harmonics. Term (c) and (d) represent third-order IMD.
The result clearly indicates that IMD and crossmodulation
only occur on a curved transfer characteristic with cubic
terms like term (c) and (d) in Equation 7. In contrast a
transfer characteristic with a linear and quadratic portion
generates the mixing products (sum and difference) and the
harmonics of the input signals.
SOME SIMPLE RELATIONSHIPS
Intermodulation distortion occurs at frequencies that are the
sum and/or difference of integer multiple of the fundamental
frequencies. For example, assume a composite signal has
fundamental frequencies ωl and ω2. Distortion products will
occur at frequencies aωl±bω2 where a and b = 0, 1, 2, 3, …
The following table illustrates this relationship.
K 2 (V IN )2 = K 2 (E12 sin 2 ω1t + E 22 sin 2 ω 2 t +
2E1E 2 sin 2 ω1t(sin ω 2 t))
(6)
(4)
2nd-Order Frequencies
ω1 – ω2
ω1 + ω2
TABLE I.
2
3rd-Order Frequencies
2ω1 + ω2
2ω1 – ω2
2ω2 + ω1
2ω2 – ω1
Amplitude of 3rd IMD Tones = 3K 3 E12 E 2 / 2
Most IMD can be filtered out. However, if the input tones
are of similar frequencies, the third-order IMD (2ωl – ω2,
2ω2 – ωl) will be very close to the fundamental frequencies
and cannot be easily filtered. Third-order IMD is of most
concern in narrow bandwidth applications. Second-order
IMD is of greater concern in broad bandwidth applications.
Figure 2 below illustrates on a spectrum analyzer the output
spectrum of two frequencies (fl, f2) applied to the non-linear
transfer characteristic of a mixer with an overdrive level of
10dB.
Converting to dB provides:
Amplitude of 3rd IMD tone =
20 log(3K 3 / 2) + 20 log(E12 ) + 20 log(E 2 )
Amplitude of 3rd IMD Tone (dB) =
constant + 2E1 + E 2
(8)
where E1 and E 2 are expressed in dB
Equation 8 shows that if the input level (dB) increases, the
level of the third-order IM products increases three times
faster.
Figure 4 shows the graphic presentation of the theoretical
increase of the IMD products when the level increases. The
desired output of an amplifier and any IMD can be represented by two straight lines of different slopes. The desired
output lines have a slope of +1, any IMD has a slope of n,
where n is the order of IMD.
Consequently, the third-order IMD has a slope of 3.
As can be seen in Figure 4 for low level input signals the
output tracks the input. At higher input levels Gain Compression occurs at the point where the actual output power
drops below the ideal. The –1dB gain compression point is
a well accepted performance parameter for RF amplifiers.
The intercept point can be found at the intersection of the
theoretical line extension of output signal and IMD. The
intercept point can be determined from the value of the
harmonic suppression (∆IM) which must be determined
experimentally. Equation 9 illustrates this relationship.
FIGURE 2. Generation of Harmonics and IMD.
Figure 3 shows the 2nd and 3rd IMDs for the condition in
which the fundamental terms (ωl and ω2) are 20 and 21MHz
sinewaves.
70
60
Fundamental Signals
20MHz = ω1; 21MHz = ω2
50
30dBm
IP2
30
20
3rd IMD
Harmonic
Suppression
2nd IMD
1MHz = ω2 – ω1
5dBm
IP3
2
10
IM
3rd IMDs
22MHz = 2ω2 – ω1
19MHz = 2ω1 – ω2
0
2nd IMD
41MHz = ω2 + ω1
1dB
Compression
–10
dBm
Amplitude
40
–20
IM
3
–30
–70
FIGURE 3. Relationship Between Fundamentals and IMDs.
–80
al
gn
≥70dBc IM3
–60
Si
–50
≥60dBc IM2
–40
Frequency
–90
INTERCEPT POINT
–100
The location of the IMDs relative to the fundamental tones
has now been defined. The relationship of amplitudes of the
IMD tones depends on the order of the IMD. The coefficients of the third-order IMD term in Equation 7 can be used
as a starting point in the analysis.
–120
–60 –50 –40 –30 –20 –10 0 10 20 30 40 50 60 –70
–18dBm
5dBm
FIGURE 4. Relationship Between Fundamental and 3rd
IMD.
3
Intercept Point = (Hamonic Suppression) / (N – 1) +
(Power of One Fundamental at Output of Amplifier) (9)
By rearranging the Equation 9 the magnitude of third-order
products can be easily calculated for any output power
(dBm) when the intercept point is known.
Third IMD = 2 (OIP3 – PO)
Third IMD = third-order intermodulation ration
below each output tone (dB)
(10)
One can also make a judgment about the dynamic range of
an amplifier with the knowledge about the IP value and the
sensitivity (amplifier noise power). A limit for the best
distortion-free dynamic range is available when the IM
products equal the sensitivity.
For a sensitivity of P N = –140dBm at measurement
BW = 10Hz for an input mixer and OIP3 = +5dBm, the best
input level can be calculated with Equation 11.
(N − 1) • OIP + P N
N
2 • 5 + (−140)
=
= − 43dBm
3
P IN =
1. Set the amplitude of the two inputs equal with the
power meter.
2. Check for gain compression by reducing the signal
power of both fundamentals by 1dB, then checking to
make sure that the 3rd IMD tone is reduced by 3dB. If
past the compression point (see Figure 2), then the
amplitude of the input to the amplifier should be
reduced (repeat Step 1).
3. Measure the harmonic suppression of the 3rd IMD
tone on the spectrum analyzer. This is the difference
between the magnitude of the fundamental and the 3rd
IMD (See Figure 1).
4. Measure the amplitude of a fundamental signal at the
output of the DUT by disconnecting one of the signal
generators.
5. Calculate the intercept point using Equation 9.
(11)
The distortion free dynamic range results with Equation 12
to 90dB for narrow spaced input signals.
(N1 ) • (OIP − P N )
N
2 •135
=
= 90dB
3
DETERMINING HARMONIC SUPPRESSION
The test system used to measure harmonic suppression is
diagrammed below.
∆IM =
THIRD-ORDER RESULTS
FOR THE OPA622 AND OPA623
The 3rd IMD intercept points are measured for the OPA622/
623 using fundamental input frequencies from 5MHz to
250MHz with 1MHz spacing between tones. All parts were
set up in a gain of +2 and were driven into a 100Ω load.
(12)
Signal
Generator A
6dB
Attenuator
Spectrum
Analyzer
Filter
Power
Divider
6dB
Attenuator
3dB
Attenuator
Power
Divider
DUT
Filter
Power
Meter
Signal
Generator B
(Attenuators are used to limit the IMD of the signal generator setup; for every 1dB
attenuation of the fundamental signs, the nth order IMD is reduced by n dB.)
FIGURE 5. Test Setup to Measure Harmonic Suppression.
4
Power
Meter
Non Inverting
R3
100Ω
RI
180Ω
In+
OPA623
R2
100Ω
RO
51Ω
7
3
2
6
Out
4
R´O
R1
300Ω
+5V
R2
300Ω
7
C1
470pF
C3
10nF
+
C5
2.2µF
C2
470pF
C4
10nF
+
C6
2.2µF
Gnd
–5V
4
FIGURE 6. Circuit Schematic DEM-OPA623-1GC Used for IMD Performance Tests.
OPA623
IM3 AND IP3 vs FREQUENCY (0dBm Input)
OPA623
IM3 AND IP3 vs FREQUENCY (–10dBm Input)
40
40
20
20
IP3
0
IP3
P0
–20
dB
dB
0
P0
–20
IM3
IM3
–40
–40
–60
–60
–80
–80
0
50
100
150
200
250
0
300
50
100
150
200
250
Frequency (MHz)
Frequency (MHz)
FIGURE 8. IM3 and IP3 vs Frequency (0dBm Input).
FIGURE 7. IM3 and IP3 vs Frequency (–10dBm Input).
5
300
OPA623
IM3 AND IP3 vs FREQUENCY (10dBm Input)
40
20
20
IP3
P0
30
IP3
25
0
20
dB
IM3
–20
35
–20
P0
15
IM3
–40
–40
10
IQ
–60
–60
5
0
–80
–80
–40
0
50
100
150
200
250
Quiescient Current, (IQmA)
40
0
dB
OPA623
IM3 AND IP3 vs INPUT LEVEL (100MHz)
–30
–20
300
–10
0
10
20
Input Level (dBm)
Frequency (MHz)
FIGURE 9. IM3 and IP3 vs Frequency (10dBm Input).
FIGURE 11. IM3 and IP3 vs Input Level (100MHz).
OPA623
IM3 AND IP3 vs INPUT LEVEL (50MHz)
OPA623
IM3 AND IP3 vs INPUT LEVEL (200MHz)
P0
80
25
0
dB
20
–20
Iq
15
IM3
–40
10
–60
5
–40
–30
–20
–10
0
10
50
60
IQ
40
40
20
30
IP3
0
P0
–20
20
IMD
–40
10
–60
0
–80
60
0
–80
20
–40
Input Level (dBm)
–30
–20
–10
0
10
20
Input Level (dBm)
FIGURE 10. IM3 and IP3 vs Input Level (50MHz).
FIGURE 12. IM3 and IP3 vs Input Level (200MHz).
6
Quiescient Current, (IQmA)
20
100
30
dB
IP3
35
Quiescent Current, IQ, (mA)
40
–VCC +VCC
+VCC OUT
1pF
COTA
5
RQC
390Ω
–VCC
2
12
10
11
Biasing
RL
50Ω
9
Out Z O = 50
OB
RIN
50Ω
OPA622
ZO = 50 In POS
RSOURCE
= 50Ω
RL2
100Ω
RLR
150Ω
4
OTA
R1
330Ω
RL1
100Ω
3
FB
8
13
6
ROG
150Ω
–VCC OUT
R2
330Ω
12
R9
10Ω
11
C1
470pF
C2
10nF
C6
470pF
C5
10nF
+
+5V
C3
2.2µF
Gnd
R8
10Ω
+
C4
2.2µF
–5V
6
5
FIGURE 13. Circuit Schematic DEM-OPA622-1GC Used for IMD Performance Tests.
7
OPA622
IM3 AND IP3 vs FREQUENCY (–10dBm Input)
60
35
40
30
20
10
20
IP3
dB
dB
0
–10
–20
P0
–30
25
IP3
20
0
IQ
P0
–20
IM3
15
IM3
–40
–50
–40
10
–60
5
Quiescent Current, IQ (mA)
OPA622
IM3 AND IP3 vs INPUT LEVEL (50MHz)
30
–60
0
–80
–70
100
150
200
250
–40
300
–30
–20
FIGURE 14. IM3 and IP3 vs Frequency (–10dBm Input).
10
20
FIGURE 17. IM3 and IP3 vs Input Level (50MHz).
OPA622
IM3 AND IP3 vs FREQUENCY (0dBm Input)
OPA622
IM3 AND IP3 vs INPUT LEVEL (100MHz)
30
50
30
20
20
10
10
IP3
0
P0
–10
–10
–20
dB
0
dB
0
Input Level (MHz)
Frequency (MHz)
IM3
IP3
30
P0
25
IQ
–30
–40
–40
–50
–50
–60
–60
20
IM3
–20
–30
15
10
5
0
–70
–70
0
50
100
150
200
250
–40
300
–30
–20
–10
0
10
20
Input Level (dBm)
Frequency (MHz)
FIGURE 15. IM3 and IP3 vs Frequency (0dBm Input).
FIGURE 18. IM3 and IP3 vs Input Level (100MHz).
OPA622
IM3 AND IP3 vs FREQUENCY (10dBm Input)
OPA622
IM3 AND IP3 vs INPUT LEVEL (200MHz)
30
30
20
50
20
10
IP3
0
P0
25
0
–10
IM3
–20
30
10
dB
dB
–10
–30
IP3
–10
15
–30
–40
–50
–50
–60
–60
20
IM3
–20
–40
IQ
P0
10
5
0
–70
–70
0
50
100
150
200
Quiescent Current, IQ (mA)
50
250
–40
300
–30
–20
–10
0
10
20
Input Level (dBm)
Frequency (MHz)
FIGURE 16. IM3 and IP3 vs Input Level (50MHz).
FIGURE 19. IM3 and IP3 vs Input Level (200MHz).
8
Quiescent Current IQ (mA)
0
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