Spectrum analyzer dynamic range

[salamander]

Hi guys. I have a quiz question I can't find an answer to. I believe it's really simple, I'm just unable to find the right solution.

The question

What is the maximum dynamic range of spectrum analyzer R&S FSL3 on a frequency of 1,25GHz, for which we can consider it's behavior linear.
Noise is -33dBuV, used filter has a range of 300Hz.

Thanks for any help. (I don't expect a direct solution, but at least point me right direction)

BTW: I'm not an electronics engineer

FSL3 datasheet: https://www.testworld.com/wp-content/uploads/specifications-rohde-and-schwarz-fsl3-fsl6-fsl18-spectrum-analyzers.pdf

[technogeeky]

WARNING: I started this off as a general answer to your question because I didn't know the answer. So this is not for you, but for me, future me, and future people to form a better formatted answer to the general question: what is the equation for spectrum analyzer dynamic range? I got bored and stopped before I finished.



So a ideal spectrum analyzer has a both a maximum power level and an absolute-minimum power level (or noise floor, or displayed average noise level (DANL)). An ideal spectrum analyzer would have an ideal display, an ideal mixer, and presumably ideal preamplifier, attenuators, and amplifiers.

It looks like the equation the overall dynamic range of a spectrum analyzer is:

range_measurement + range_display +  noise_DANL + noise_spurious + noise_phase = Dynamic Range

You've heard of some of these before:

• range_display is borne from the fact that the any display device has a maximum and minimum intensity.
• range_measurement is the difference between the largest signal from the most attenuated input setting to the smallest signal from the least attenuated setting.
• noise_spurious is the amplitude of the spurious tones created by the instrument's amplifiers and mixers.
• noise_DANL is the Displayed Average Noise Level, or noise floor or sensitivity.*
• noise_phase is the instability caused by mixing the signal with the inherently unstable local oscillator (LO)

• HINT: Ignoring range_display, notice the impact from each component of the dynamic range decreases from left to right:
• range_measurement (-151dBm and up from Figure 1)
• noise_DANL (-135 dBm and up)
• noise_spurious (97 and 90 dB of range above the -135dBm floor)
• noise_phase (the 80 dB of range left over when you set your reference to minimize phase noise)

• HINT: noise_DANL is the "key" property when measuring two signals that are far apart in frequency (in contrast to phase noise)
• HINT: noise_phase behaves like third order inter-modulation (TOI) distortion: it is most significant when the input signal has two tones that are nearby to each other (less than 1 MHz) -- at least for purposes of dynamic range

Even if we don't fully understand all of these, we use some relationships, hints, and assumptions to simplify our question:

First, we work under the assumption that a wide signal is similar enough to two thin signals spaced apart by the width. This is a simplification used in tons of testing procedures, and it's the analysis of inter-modulation distortion. The two unhighlithed tones f₁ and f₂ are the inputs. I think, however, that in your specific case we don't need to consider this both because it doesn't mention two tones and because the RBW is only 300 Hz, which is much smaller than 1 MHz.

According to this paper (from which this response is almost entirely plagiarized), after we set our reference (mixer level) just right (right where our second-order and third-order distortion curves meet), then the dynamic range is equal to the equality of these two equations:

range_3rd = (2/3) * ( DANL_actual - TOI )
range_2nd = (1/2) * ( DANL_actual - SHI )

TOI^a = mixer level - (1/2) (distortion products in dBc)
SHI^b = mixer level -         (distortion products in dBc)
DANL_actual = DANL_{at 1 Hz} - 10 log ( DANL_{at your RBW} / DANL_{at 1 Hz} )

So, having typed all of this out, I think you have enough to know where to look in the manual you linked to find the DANL at 1 Hz, then find the right mixer level at 1.2 GHz; converting your answer to the 300 Hz RBW (which happens to be the minimum RBW for that instrument).

• ^a Third Order Intercept (point). Also called IP3.
• ^b Second Harmonic Intercept (point). Also called SOI or IP2.
• * DANL actually has a physical absolute minimum of -174 dBm derived from its defining equation:
  
  DANL_min = kTB.
  
  
  • k is Boltzmann's Constant (which has dimensions of [energy] / [temperature], I'm sure I do need to remind you. I needed to remind me.).
  • T is temperature which has dimensions of ... [temperature], and units of [Kelvin].
  • B is bandwidth which has units of [frequency], we're going to use [Hertz].
  
  Apparently, if you are bored enough to multiply these together, (or even to just do the dimensional analysis, honestly) you will find that these are in units of power and calculated at room temperature and 1 Hz (a standard for some reason), you really do get -174 dBm.

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