THE RELATIONSHIP OF INTERCEPT POINTS AND COMPOSITE DISTORTIONS
(Revised Feburary 18, 1998)
Amplifiers, mixers, diode attenuators, and some passive devices can generate intermodulation distortion. These distortion products are a result of a nonlinear transfer characteristic.
A common specification, related to distortion, for amplifiers and mixers is the Intercept Point. If the input Vs output of a device is displayed graphically on a dB Vs dB scale, the slope of the linear portion will be 1. If second order distortion products are displayed on the same scale they will have a slope of 2, third order distortion products will have a slope of 3, etc. In most cases distortion products above third order are not important but these rules are still valid.
The Intercept Point is the point where the linear extension of the particular distortion intersects the linear extension of the input Vs output line. Usually intercept points are given in terms of output power but in some cases, for example mixers, intercept points are given in terms of input power. When making distortion calculations, it is necessary to specify, or at least be consistent, as to where (input or output) the results apply.
To be more correct the intercept point should be named the Two Tone Intercept point because two tones are used as the signal source. Two tones will generate third order distortion products 3A, 3B, 2A+ B, 2A- B, 2B+ A and 2B- A. This method of measuring distortion was developed so that narrow band amplifiers could be measured. The only third order products that fall in band, in narrow band amplifier, are 2A- B and 2B- A.
Figure 1, TWO TONE SECOND AND THIRD ORDER DISTORTION PRODUCTS. INPUT LEVEL FOR ONE TONE, VS OUTPUT SIGNALS AND DISTORTIONS RELATIVE TO ONE TONE
The method of making the measurement is to insert two closely spaced equal level carriers into the device under test. The distortion products are then measured and compared with the level of one of the signals.
The graphic representation of the distortions is valuable because it allows insight into the behavior of the distortion products.
If the signal levels are 20 dB below the third order intercept point, then the third order distortion will be 40 dB below the signal.
In a similar way it is obvious that if the signal levels are 20 dB below the second order intercept point, then the second order distortion will be 20 dB below the signal.
If we now consider the case of many carriers in a broad band system, the problem becomes more complicated. Consider a CATV system with many equally spaced carriers. Now we note that the distortion products 2A- B and 2B- A are no longer important. This is because there are fewer of them and they are one half the amplitude (- 6 dB) of the now dominant distortion products A+ /-B+/- C where A<B<C. (See MATRIX TECHNICAL NOTE MTN-108) These beats are referred to as COMPOSITE TRIPLE BEAT or COMPOSITE THIRD ORDER distortions. They are named composite distortions because they are made up of a composite of discrete distortions. They fall in a narrow range of frequencies near the carrier frequency and are measured as a group. The carriers are assumed spaced by some frequency (usually 6 MHz) and are not coherent. If they were coherent (or phase locked) the beats would also be coherent. The frequency variation of the carriers, which is on the order of a few KHz, causes the beats to have a band-spread of about 20 KHz. The spectrum of the beats resembles noise because it is made up of many carriers. In general the power in the composite of the beats is the sum of all the power in the individual beats. It is only necessary to find the power on one distortion beat and the total number of beats to determine the composite beat.
COMPOSITE THIRD ORDER DISTORTION
For equally spaced carriers, the total number of composite distortion products of the A+ /-B+/- C variety can be closely approximated by;
Number of beats (mid band) = 3N2/8
Number of beats (band edge) = N2/4
The beats that dominate multiple channel systems are the A+ /-B+/- C beats because these beats are 6 dB stronger than the 2A- B and 2B- A beats.
Consider the following example, an amplifier is operating with 20 channels with the level of each carrier 40 dB below the intercept point. We know from our definition of intercept point that the 2A- B distortions must be -80 dB below carriers and the A+ /-B+/- C distortions must be - 80+6 = - 74 dB below the carrier. We also know that in the middle of the band, there are 3N2/8 distortion beats.
For example if: N=20
Number of beats (mid band) = 3N2/8 = 150 = 21.76 dB (in terms of power ratio)
We can assume that all the distortion beats have the same amplitude and will add as powers. In the example above the A+ /-B+/- C products were - 74 dB below the carrier but we have 150 of them and if they add as powers then the CTB will be - 74+21.76 = - 52.24 dB below the carrier.
In general:
CTB(dB) = - 2(Pi - Ps)dB + 6dB + 10 LOG (3N2/8)dB Mid band
CTB(dB) = - 2(Pi - Ps)dB + 6dB + 10 LOG (N2/4)dB Band edge
CTB = Composite third order distortion (dB)
Pi = Power level at the third order intercept point (dBm)
Ps = Power level of each carrier (dBm)
N = Total number of carriers
COMPOSIT SECOND ORDER DISTORTION
It is now obvious that a similar approach can be used to calculate the composite second order (CSO) distortion from the second order intercept point.
Note that the discrete second order product has the same magnitude as the individual products in the composite distortion.
Using the relations found in MATRIX TECHNICAL NOTE MTN-108
Number of beats (Below carrier) = N(1- (f/(fH - fL + d)))
Number of beats (Above carrier) = (N- 1)(f - 2fL - d)/(fH - fL - d)
In general:
CSO(dB) = (Pi - Ps )dB + 10 LOG(Number of Distortion products)dB
Pi = Power level at the second order intercept point (dBm)
Ps = Power level of each carrier (dBm)
N = Number of carriers
f = Frequency of distortion product in MHz
fH = Frequency of highest channel in MHz
fL = Frequency of lowest channel in MHz
d = Frequency separation between channels in MHz
There are far fewer second order beats than third order beats but the magnitude of each beat may be stronger that the third order beat. In most high quality amplifiers push-pull circuits are used to reduce the second order distortion. This has the result of increasing the level of the second order intercept point but does not alter its slope.
CROSSMODULATION
X-MOD or crossmodulation is a third order distortion that is also related to the third order intercept point. It can also be considered a composite distortion similar to CSO and CTB. If the crossmodulation is the result of only the third order nonlinearity determined by the intercept point then;
X-MOD= - 2(Pi - Ps)dB + 6dB + 20 LOG(N)dB
X-MOD = Crossmodulation below 100% modulation (dB)
Pi = Power level at the third order intercept point (dBm)
Ps = Power level of each carrier (dBm)
N = Total number of carriers
Note that the distortion is independent of the carrier frequency.
POSSIBLE SOURCES OF ERROR
It is now important to emphasize some of the problems related to the measurement of CSO, CTB, and crossmodulation.
The common method of making composite distortion measurements uses a spectrum analyzer operating in the LOG display mode. In this mode, spectrum analyzers measure noise and noise-like signals in error. They measure noise as approximately 2.5 dB weaker than the actual power.
The spectrum analyzer method has become the "definition" of the distortion. This may result in discrepancies among the measuring methods. Great caution is required when correlating or interpreting measurements by other methods.
Crossmodulation measurements can also be a problem. Using a spectrum analyzer to measure the distortion sidebands directly can result in large errors. The desired measurement is actually amplitude crossmodulation. Many active devices generate phase crossmodulation with magnitudes that are 30 dB above the amplitude crossmodulation. The spectrum analyzer can not differentiate between the amplitude and phase sidebands and as a result great errors can occur. There are several valid methods for measuring crossmodulation, one is covered in MTN-110.
The equations used for calculating the distortion products were derived by Dr. Thomas B. Warren.
Interpretations, opinions, explanations and other errors are the responsibility of Jack Kouzoujian, Matrix Test Equipment Inc.
