As an example, the accuracy and dynamic range specifications of an N9020A MXA signal analyzer can be used to determine what test line limit can set for making a TOI measurement of a DUT that has a TOI specification of +22 dBm at a 1-GHz carrier frequency.

It is first necessary to determine an optimum carrier level to test the DUT. A -10 dBm output level from the DUT should produce a TOI product of -64 dBc (at most) below the level of the fundamental frequency amplitudes. This can be found by the following relationship:

TOI = Afund - (1/2)D   (1)


D = 2(Afund - TOI)   (2)


Afund is the amplitude of the fundamental frequency tone and D is the difference in amplitude of the fundamental and distortion product in dBc.

Testing the DUT to a limit of -64 dBc, however, would not include the measurement uncertainties that should be included in a pass/fail test limit. These include uncertainties from the TOI dynamic range of the signal analyzer and amplitude uncertainties in a relative amplitude measurement.

The dynamic range of the MXA signal analyzer should also be considered when evaluating its TOI measurement capabilities. The TOI specification is +16 dBm at a fundamental frequency of 1 GHz.

Understanding Measurement Uncertainties in Spectrum Analysis, Table 2

This specification is based upon the mixer level and not the level at the input. The mixer level is given below:

Mixer Level = Fundamental Level - input attenuation - external attenuation

Substituting Afund with mixer level yields:

D = 2(Mixer Level -TOI)   (3)

Equation 3 explains that increasing the spectrum analyzer input attenuation improves the signal analyzer’s internal distortion products. As an example, as shown in Equation 4, the internal attenuation can be increased to 16 dB with no external attenuation to calculate the distortion level (in dBc) with a fundamental level of -10 dBm from the DUT:

D = 2(-26 dBm - 16 dBm) = -84 dBc   (4)

By knowing the dynamic range of the signal analyzer’s TOI, it is possible to stay with an input level from the DUT of -10 dBm and the instrument’s internal attenuation set to 16 dB will have a 20-dB margin between the DUT distortion products and the signal analyzer’s internally generated distortion products. In a worst-case scenario, the internal and DUT distortion products could sum together in phase to decrease the dynamic range by 20LOG[1 + 10(-20/20)] or 0.83 dB or increase the dynamic range by 20LOG[1 + 10(-20/20)] or -0.46 dB. This uncertainty in the measurement result due to dynamic range would need to be included in the test limit to make for a more stringent test of device performance. However, adding an additional 10-dB attenuation to the 16-dB input attenuation lowers this uncertainty to +0.27 dB/-0.28 dB. This significantly lowers the dynamic range uncertainty portion of the test limit.

When using the narrow spans normally part of TOI measurements, the measurement uncertainty is dominated by the display scale fidelity of the test instrument. Modern spectrum analyzers with all-digital intermediate-frequency (IF) circuitry have extremely good linearity when compared with analog IF circuitry used in the past. The display-scale-fidelity specification is approximately ±0.07 dB.

These worst-case uncertainties can now be added to a DUT specification and be used to set a test limit that ensures that the dynamic range and accuracy of the signal analyzer do not cause yield issues or result in a DUTpassing a production test that should have failed the test. In many cases, additional uncertainties apply that were not used in this example such as environmental uncertainties or measurement uncertainties from other test devices in the system.


Modern test equipment manufacturers go to great lengths to ensure that the user is given sufficient specifications to determine measurement uncertainties for a particular measurement. These instrument specifications should enable the user to not only know what the uncertainties are, but how to improve upon them in many cases.