• Review sections 1.2 and 1.3 IQ theory

  • Open the GRC patch ra5.grc. This flowgraph implements the mathematics on the last page of the IQ theory document.

    • The USRP source does IQ downconversion on the WBX daughtercard and outputs the complex signals I(t) + jQ(t).

    • This output is connected to 4 blocks that extract the magnitude, phase, real and imaginary parts of the complex signal, as well as an XY scope.

    • The USRP source is tuned to a fixed frequency of 200 MHz, i.e. the LO frequency synthesizer in the WBX daughtercard is set to 200 MHz.

  • Double‐click the USRP source block to bring up a window with all of the USRP parameters. This general I/Q receiver is set up to receive a signal in a range around 200 MHz at level -40 dBm from the signal generator at the back of the lab.

  • Execute the flowgraph. Observe the Output Display window with 5 tabs labelled Scope Plot, Magnitude, Phase, Real and Imaginary.

    • The Scope Plot tab should show a circle

    • Magnitude will show a (noisy) DC level

    • Phase will show a phase ramp wrapping between -π and π

    • Real and Imaginary will show (noisy) sine waves.

  • The scope autorange may need to be switched off and the time base adjusted to get good displays.

  • Determine the frequency fb of the sine waves using the Phase display as well as the Real and Imaginary displays by placing your mouse cursor over the scope plot to show the time offset at different points on the waveform. This frequency fb represents the offset between the received RF signal fc and the USRP local oscillator fLO, so that

    fb = fc - fLO

  • Confirm that fb is as expected.

  • The USRP source block has the clock source set to use an external 10 MHz clock reference frequency, and the same external reference is used for the signal generator. Thus the frequency difference between the USRP source block (local oscillator) and signal generator RF frequency will be observed to be exactly as expected from their respective frequency settings.

    • If we change the USRP source block to use an internal clock reference, then expect to observe some frequency error between the signal generator and the USRP frequency settings as they are running from independent oscillators.

    • Try changing the USRP clock source to internal and repeat the frequency measurement of the I and Q outputs.

  • Review link budget notes with particular attention to equation (14).

  • When you tune the receiver to a frequency where there is no station broadcasting, there is still a residual noise floor visible on the spectrum display. The noise level can be estimated by looking at the display and observing the level in dBm (dB relative to one milliwatt). This is thermal noise that is calculated from the formula

    Pnoise = kT(S/N)WF

    where

    • k is Boltzmann's constant

    • T is the noise temperature, typically 290 degrees Kelvin

    • W is the bandwidth in Hz and

    • F is a dimensionless noise figure representing imperfect amplifiers.

  • By substituting values for k and T and taking logs of both sides of this formula, we can write in dB:

    Pnoise = -228.6 + T + (S/N) + W + F.

  • Estimate the noise figure of the receiver based on the noise level in dBm on the computer spectrum display and the receiver bandwidth of 250 KHz.

    • All the variables in the noise figure equation except F are known or can be measured, so the equation can be solved for F.

    • The specified value for the URSP with WBX board is 5.5 dB.