One of the methods to characterize non-linearity of a device is to excite its input with a two-tone signal and measure the power of undesired distortion products that are generated at the output. While a single tone at the input of such DUT would generate harmonics at integer multiple of tone frequency, a two-tone signal, with tone frequencies at f1 and f2, would generate distortion products at frequencies which are linear combination of f1 and f2. Such distortion products are called intermodulation products or intermods. The following figure shows a spectrum containing fundamental tones and intermods.

The input-output voltage relationship of such non-linear devices can be expressed as a Taylor series as shown in the following equation:

Let the tone frequencies in the input signal be f1 and f2, initial phases be φ1 and φ2 and amplitudes be a1 and a2. You can calculate the input and output voltages using the following equations:

The second order term in equation (3) generates second order harmonics and second order intermods. Similarly, the third order term generates third order harmonics and third order intermods. The following table lists the frequencies at which these distortion products are generated by first few terms in equation (3).

In general, nth order term will generate harmonics and intermods at frequencies:

The third-order intermods at 2f1- f2 and 2f2- f1 lie close to the fundamental tones. The third-order intermods are followed by fifth-order components at 3f1-2f2 and 3f2-2f1, followed by seventh-order components 4f1-3f2 and 4f2-3f1, and so on. These consecutive odd order intermods are separated in frequency by the fundamental tone separation as shown in the following equation:

Δf = f2 - f1

Intercept Points

The following figure shows the output power one of the fundamental tones and one of the third order intermods plotted against input power of the fundamental tone, provided that the two input tones are of equal power.

These plots are straight lines for low input powers and deviate from the straight line behavior as input power is increased due to gain compression in real world DUTs. If these straight lines are extrapolated, they intersect at a theoretical point known as the third order intercept (IP3 or TOI). At this point, the output power of the fundamental tone is equal to the output power of the third order intermod. This output power is called third order output intercept power (OIP3) and the corresponding tone input power is called third order input intercept power (IIP3).

In general, you can define IPn, IIPn, and OIPn points for any nth order intermod. The IM measurement computes only OIPn powers. The IPn point acts as a figure of merit when evaluating multiple DUTs, where a higher IPn DUT is expected to provide a better signal-to-distortion ratio.

When the input signal consists of two tones of unequal powers, the nth order intermods will be at different power levels. This can also happen when the frequency response of the DUT is not flat in the region of operation. This leads to two definitions of OIPn: nth order lower output intercept power (OIPn,lower)  and upper output intercept power (OIPn,upper) These intercept powers are computed using the following equations [2].

where,

         

The intermod relative powers are computed as follows:

Δ P n , l o w e r   i n t e r m o d = P n , l o w e r   i n t e r m o d - n - 1 P o u t p u t , l o w e r + P o u t p u t , u p p e r n                                   ( 6 )
Δ P n , u p p e r   i n t e r m o d = P n , u p p e r   i n t e r m o d - n - 1 P o u t p u t , u p p e r + P o u t p u t , l o w e r n                                   ( 7 )

where,

ΔPn,lower intermod represents the lower intermod relative power for nth intermod

ΔPn,upper intermod represents the upper intermod relative power for nth intermod

Hardware Setup

Although a single generator can be used to generate a two-tone signal, the resultant signal may contain intermods generated by non-linear components of the generator itself. A better way to generate a clean two-tone signal is by using two independent generators with a power combiner. The following figure shows a typical hardware setup for IM measurement.

The power combiner should have high return loss at all three ports, high isolation among the input ports and high reverse isolation from output port to the input ports. To further increase the return losses at the ports of the power combiner, you can use isolators or directional couplers.

Measurement Configuration

The RFmxSpecAn IM measurement allows you to configure two fundamental tone frequencies. You can configure the intermod frequencies by setting Auto Intermods Setup Enabled property to either True or False.

Auto Intermods Setup Enabled

When you set the Auto Intermods Setup Enabled property to True, the measurement auto-computes the intermod frequencies by using Maximum Intermod Order property, which you can set to either 3, 5, 7, or 9. This mode supports measurements of only odd order upper and lower intermods that are close to the fundamental tones. When you set the Auto Intermods Setup Enabled property to False, you can manually configure each intermod by setting intermod enabled/disabled, intermod order, intermod side, lower and upper intermod frequencies, and number of intermods. The measurement ignores the Maximum Intermod Order property in this mode. This mode allows measurement of even order intermods as well.

Measurement Method

The RFmxSpecAn IM measurement supports the following measurement methods to cater to multiple use cases:

  • Normal—The RFmxSpecAn IM measurement acquires the spectrum using same signal analyzer settings across frequency bands. NI recommends this method when fundamental tone separation is not large and intermod powers are high enough to be measured accurately without using hardware specific optimizations like IF filters and IF gain. Supported Analyzers: PXIe-5644/5645/5646, PXIe-5663/5665, PXIe-5668
  • Dynamic Range—Use this measurement method to maximize the dynamic range of digitizer when measuring low power intermods in presence of high power two-tone signal. The following are the relevant impairments reducing the dynamic range of the digitizer when measuring intermods:
    • Quantization error due to the inability of using the full-scale of the digitizer. To utilize the full-scale of the digitizer more efficiently when measuring low power intermods, narrowband IF filters are used to isolate the intermod of interest while attenuating any power leakage from the two-tone signal. After knocking out the power leakage from the two-tones, sufficient IF gain is applied to the intermod, thereby increasing its power to match the full-scale of the digitizer.
    • Intermods generated by the digitizer due to the fundamental tones also impede its dynamic range. Dynamic Range measurement method eliminates the intermods generated by the digitizer by using narrowband IF filters while measuring the intermods, knocking out the high power fundamental tones before the signal reaches the digitizer.
    Note
    • The tone separation should be more than the minimum IF filter bandwidth of the signal analyzer so that intermods can be isolated from tones before digitization.
    • No IF gain is applied when measuring fundamental tones.
    • IF filter used for an intermod may vary based on the signal analyzer and the proximity of that intermod to the fundamental tones. A narrowband IF filter is used for intermods close to the fundamental tones. A wider IF filter is used for intermods that are farther from the fundamental tones to reduce measurement time.
    • This method involves multiple acquisitions, with each tone and intermod having separate acquisition. Span of each acquisition is given by following equation:
      S p a n p e r   a c q u i s i t i o n = m i n i m u m   ∆ f ,   1   M H z                                               ( 8 )

    Supported Analyzers: PXIe-5665, PXIe-5668

  • Segmented—This method is similar to Dynamic Range method, except that no hardware-specific optimizations are applied. This method acquires spectrum only around frequencies of interest, and is recommended when fundamental tone separation is large and measurement speed is desirable. The span of each segment is given by equation (8). Supported Analyzers: PXIe-5644/5645/5646, NI 5663/5665, PXIe-5668
    Note Dynamic Range method is not supported when PXIe-5668 is used with PXIe-5698 preamp.

Recommended Settings

You can improve the dynamic range of the measurement by setting the RF input attenuation such that the mixer operates at optimal operating level. Refer to the dynamic range chart of the device mentioned in the device specification to know the optimum mixer level.

M i x e r   l e v e l = R e f e r e n c e   l e v e l - R F   A t t e n u a t i o n                                 ( 9 )

For a given reference level, RF attenuation can be varied to check if the distortion from first mixer in the signal analyzer has significant contribution to intermod generated by the DUT. Increasing RF attenuation decreases the power level at the first mixer, thereby reducing the distortion introduced by that mixer. If an increase in RF attenuation decreases the intermod power, then analyzer is contributing to the distortion. However, if intermod power remains constant with increase in RF attenuation, then the measured distortion can be attributed to the DUT.

References

[1]Egan, William F. Practical RF system design. John Wiley & Sons, 2004.

[2]Kundert, Ken. "Accurate and Rapid Measurement of IP2 and IP3."Designer’s Guide Consulting, 2006.