Phase Noise Theory: System Calibration

Spectrum Analyser Calibration

It is desirable to calibrate the combined spectrum analyser plus mixer preamp response to noise. This is particularly critical when a PC sound card is used as a spectrum analyser. The above circuit buffers the Johnson noise of a 150K resistor (50nV/√Hz) and provides 2 outputs (50nV/√Hz and 5nV/√Hz) with 50 ohm source impedance. The circuit is battery powered to avoid ground loops. The rail splitter noise is rejected by the opamp CMRR. Circuit output noise increases by 1dB at 10Hz (due to the opamp's input voltage flicker noise) and has a high frequency 3dB cutoff at 200kHz due to the opamp common mode input capacitance.

Low flicker noise Cross power spectrum noise calibration source

The above circuit buffers the Johnson noise of a 150K resistor (50nV/√Hz) and provides 2 buffered 50nV/√Hz outputs with 50 ohm source impedance. The circuit can be battery powered to avoid ground loops.

The above circuit is useful when using cross correlation techniques to reduce the system noise. The cross power spectrum of the two buffered outputs is flat to well below 1Hz. The flicker voltage noise of the 2 opamps is reduced as the number of cross power spectra averaged increases.

However it is critical that a 150K resistor with very low flicker noise is used.


Phase Noise Calibration

A source with a known and flat phase noise spectrum is useful for both calibration purposes, and sanity checks of a phase noise measurement system.

The simplest implementation (shown above) uses a gaussian noise source to add noise to the output of an OCXO using a hybrid combiner (only noise source frequency components near the OCXO frequency are significant). The added gaussian, noise like thermal noise, produces equal AM and PM noise components, the AM noise is largely rejected by the phase detector. An amplified zener noise source (e.g. noise generator) can be used, the only real requirement is that its noise spectral density is stable and can be measured at the OCXO frequency. The phase noise floor produced when combined with the OCXO can then be calculated from the OCXO output the noise source spectral density and the hybrid combiner characteristics.

Similarly a Gaussian noise source with an output that is calculable from first principles is useful for spectrum analyser calibration, It is particularly useful when the noise bandwidth of the spectrum analyser isn't known. At low frequencies the amplified Johnson noise of a 150K resistor can be used.

A linear phase modulator can also be built by using a zero degree splitter to produce 2 signals at the OCXO frequency. One signal is amplitude modulated, attenuated and combined with the other signal using a 90 degree hybrid. If the attenuated output of the AM modulated signal at the 90 degree port is small compared to the signal at the 0 degree port of the 90 degree hybrid, the signal at the sum port of the 90 degree hybrid is phase modulated (there is a very small AM component). For details see reference 1. Reference 2 describes a small angle modulator that can be useful when the modulated signal is multiplied by a large factor.

Some advocate offsetting the LO frequency slightly and measuring the amplitude of resultant the beat frequency at the mixer IF port. However this technique assumes that the beat frequency output waveform is sinusoidal. When the mixer RF port is saturated the beat frequency output waveform is trapezoidal so this case measuring the beat frequency signal amplitude doesn't allow the phase detector gain to be determined.

A better method is to measure the beat frequency signal slope at the zero crossing. This technique doesn't rely on the beat frequency signal waveform being sinusoidal (or having any specific waveform). However the mixer IF signal preamp gain has to be reduced to allow this measurement without saturating the amplifier. This will change the mixer loading and hence the measured phase slope will differ from that when the amplifier gain is increased for actual phase noise measurements.

Both the above methods only measure the system gain at a single beat frequency and may not take the effect of the phase lock loop system into account. Measurement of the system gain over the full offset frequency range of interest with the amplifier gain the same as that for actual source phase noise measurements is more accurate. Either the method using the gaussian noise source or the NIST phase modulator method can be used to accurately calibrate the system gain with the same amplifier gain actually used during phase noise measurement.

An even better technique is split an low phase noise signal into 2 parts and add noise to one part via a hybrid combiner. The clean signal drives one input port of the pase detector whilst the signal with added noise drives the other input port of phase detector. This technique is used by NIST for PM (and AM) noise measurement system calibration for offset frequencies down to 1Hz. Details are described in the reference 3.



1) Method and Apparatus for Wide Band Phase Modulation

2) Ultralinear Small-Angle Phase Modulator

3) Secondary Standard for PM and AM Noise at 5, 10, and 100MHz

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