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Design Article

# Understanding the IP3 specification and linearity, Part 2

## 7/30/2012 7:41 AM EDT

Relationship between IIP and OIP
We know that IIPn and OIPn are two expressions of the same parameter (IPn). IPn is on the first-order line. Thus:

Intercept point evaluation and measurement
Take care! Those IPn points are virtual points because they do not really exist. The device saturates well before the signals reach the crossing points. All of these straight lines are, in fact, asymptotes projected from smaller values of x and y. This observation implies that we will need a practical method to extrapolate IP points.

Since we cannot apply and, therefore, measure signals that approach an IP point (because the device would be saturated well before), we need to apply a signal with smaller amplitudes. We can take the x-y figure with the axis in dB (or dBm) (Figure 6) and consider the first-order and the nth-order straight lines:

We apply an input signal, PIN; it must be small enough to not saturate the device. It will give the corresponding output, POUT. These points appear in the X and Y axis, respectively (Figure 7):

Figure 7. Power levels with straight lines for first-order and nth-order and their intercept points.

In Figure 7, PIN is the applied input signal (from the generator); POUT is the output signal at the first-order (measured); and POUT_n is the output at the nth-order (measured). We can call ΔP = POUT - POUT_n, which is the difference between measured powers at the first-order and nth- order frequencies.

If the applied signals are pure sinewaves (see the discussion above from equation 1 to equation 8), then the orders can be traced with the frequencies. Using a spectrum analyzer, one can discriminate among the various powers appearing at various frequencies.

We can now determine the relationship between the applied and measured signals versus intercept points (IPs). Figure 8 shows that one can see two triangles inside the rectangle of Figure 7.

Figure 8. IPn computation via a graphical method.

Their vertical sides must be in the same ratio as their hypotenuse slopes. Where:

Suppose now that we want to measure the IP3 performance of a given LNA, a device under test (DUT). First, we will need two independent frequency sources: generators GEN-A and GEN-B (Figure 9). The two signals will have same amplitudes and with very close frequencies, for example, ωa = 2.00GHz and ωb = 2.01GHz (thus spaced with 10MHz). We can also take 1MHz and 1.001MHz, etc. The frequency selection depends on the actual device to be tested, i.e., around 433MHz for a European ISM band or 900MHz for the GSM band.

Figure 9. Block diagram for IP3 measurement.

These two frequencies are first applied to a combiner (a sort of “adder”) and then injected into the DUT. Some filters can be found between generators and the combiner and from the combiner to the DUT. (Note: make sure that a filter is applied only to the two selected sources to the DUT.)

Using a spectrum analyzer, we observe the output. We find, of course, the two original sources at fundamental frequencies and all the harmonics and the intermodulation products (IMs).

Figure 10. Schematic view of data generated by a spectrum analyzer of IP3 measurements.

In Figure 10, POUT and ΔP are measured directly on the screen; further, OIP3 = POUT + ΔP/2.

Figure 11 shows a typical view of a spectrum analyzer screen of an IP3 measurement:

Figure 11. Spectrum analyzer screen view during IP3 test.

In Figure 11, M1 and M2 are the traces of the two fundamentals; both were measured around -11dBm (= POUT). M3 and M4 are the IM3 signals; they were both measured both approximately -45dBm.

Thus:

The results from Equation 31 show that this DUT is a standard, good LNA.

Some functions, like the first stage of a receiver RF front-end, require higher IP3 devices. This is where a device such as the MAX2062 can help. The MAX2062 dual, 50MHz to 1000MHz RF/IF VGA can be configured for many purposes such as a PA predriver, a diversity IF amplifier, and any VGA for multipath and transmitter applications. The linearity performance of this device is OIP3 of +41dBm and an OIP2 of +56dBm. Each of the two signal paths contains a 24dB amplifier and two user-programmable attenuators (one digitally controlled, one analog controlled), giving an adjustable dynamic gain range up to 64dB in steps of 1dB. Also, since all these blocks have accessible RF input and output, one can tune the circuit for best NF, best OIP3, or best combined compromises. In the MAX2062 data sheet, the OIP3 has been characterized with two RF tones of 0dBm each and separated by 1MHz. The tests were made at seven different frequencies: 50MHz, 100MHz, 200MHz, 350MHz, 450MHz, 750MHz, and 900MHz.

Understanding the effects of cascaded IPn
Once the IPn performance of an individual device is known, what happens when we combine them in a chain (Figure 12)?

Figure 12. Cascaded RF functional blocks with known IPn.

The total gain of a cascaded structure is:

The -1dB compression point (CP1 or CP1dB)
As mentioned in the introduction, IPn is the only way to characterize a device’s linearity. The -1dB compression point (CP) is also a figure of merit for measuring nonlinearity. Graphically (Figure 13), it is the point where the actual input-output response curve deviates (i.e., drops) by 1dB from the linear asymptote.

Figure 13. Graphical view of a -1dB compression point.

The -1dB compression point can also be seen as the point where the actual curve crosses the linear dropped by 1dB asymptote. As for the IP parameter, the compression point can be expressed as input (ICP1) or output (OCP1). It can also be observed that CP1 is strongly linked with the IP3 values, even though there is no strict relationship. In general,

Consider an example. The MAX2645 is configured as a PA predriver with a gain of 15.2dB. Here the input 1dB compression point (CP1) is -1.8dBm, while its IP3 under the same setup is +11.8dBm. We see that IIP3 and ICP1 differ by 13.6dB.

Conclusion
Indeed, normally one does not need the above analysis to make an IP3 measurement with a spectrum analyzer. Occasionally, however, engineers require deeper, detailed explanations when faced with an unexpected phenomenon or, perhaps worse, systematically absurd results.

Kuo-Chang Chan is director of field applications engineering in southern Europe for Maxim Integrated Products. He joined Maxim in 1999 and has more than 30 years of semiconductor industry experience in various roles from fab engineer to designer of custom analog and mixed-signal circuits. He has an MSEE from the University of Louvain in Belgium.

DanOD

8/9/2012 12:39 PM EDT

Very good article, the subject is well explained. From the results in Eq 31 you say that the DUT is a standard good LNA, is it through experience that you know what is a good and bad measurement and what value would you class as a poor performing LNA.

skir8r

8/10/2012 11:07 AM EDT

A good article which would be even better if the distinction between "dB" and "dBm" was made. The problem is hinted at between eqn. 24 and eqn. 25, but is very clear in eqns. 28, 29, & 30. The differences between signal levels should be in "dB", not "dBm".