Analyzing the Role of Local Oscillator
Phase Noise in Reciprocal Mixing

By Dale D. Henkes, ACS

Effective sensitivity and dynamic range of a receiver can be
limited by LO (local oscillator) noise sidebands translated to the IF by a
strong signal that is not far outside of the IF band.  This undesirable process, called
reciprocal mixing, is caused by the mixing of weak LO sidebands with a strong
interfering signal.  The process of
superimposing LO noise sidebands onto signals entering the mixer is a result of
the normal operation of a mixer.  It
is a function of how a mixer works and is not due to any fault of the mixer
but, instead, is a result of a non ideal noisy LO.  After the mixer, the strong interfering
signal is substantially eliminated by the IF filter but the LO phase noise,
imposed onto the interferer(s) by the mixing process of the mixer, cannot be
removed because it extends well into the IF band.

Figure 1, Receiver RF Front End (Antenna Through IF)

The schematic in Figure 1 represents a receiver front end
section from antenna through the IF filter (Port1).  Port2 in Figure 1 provides a sample of
the signal prior to passing through the IF filter (for purposes of facilitating
the simulation analysis).  The
circuit is designed to tune the 915 MHz ISM band in steps of 30 KHz channel
bandwidth.  The mixer employs high side
injection using a 1315 MHz LO to down-convert the 915 MHz received signal to
400 MHz IF (intermediate frequency).

In this article the LINC2 Visual System Architect (VSA) from
Applied Computational Sciences (ACS) will be used to demonstrate the effects of
reciprocal mixing.  The LINC2 VSA is
a schematic based system level simulator.
The VSA’s menu of components provides quick access to both linear
and non linear parts that can be easily arranged in any combination to
represent the system on the schematic page.  The LINC2 VSA system simulator is
particularly suited for analyzing many component and system performance
parameters.

Initially we will employ the LINC2 VSA simulator to analyze
the signal to noise ratio without considering LO phase noise.  Then we will introduce phase noise on
the LO and show through simulation how the phase noise is transferred to the
adjacent channel interfering signals and consequently spread into the IF band,
effectively resulting in a reduction in the apparent signal to noise ratio.

Figure 2, Some Receiver Front End Simulation Results
(LINC2 VSA Simulation of the Circuit in Figure 1)

Receiver Front End Analysis Without LO Phase Noise

The antenna delivers the desired 915 MHz signal at -113 dBm
in the presence of two interfering signals in the adjacent and alternate
channels at approximately 30 KHz and 60 KHz offset respectively.  The adjacent channel interfering signal
at 915.0305 MHz is 63 dB stronger than the desired signal.  The level of the alternate interferer
(at 915.0611 MHz) is also 63 dB above the desired.  These signals are shown at the antenna
port in Figure 1.

Referring to the VSA simulation results from Figure 2 for
the following, the noise bandwidth (NBW) of the 30 KHz IF filter is 31.1412
KHz, providing an effective noise floor at the antenna port of 10Log(1000 KT) +
10Log(NBW) + NF = -173.976 + 44.93 + 5.0417 = -124 dBm.  The front end gain is -1.6 dB, bringing
the noise floor at the output of the IF filter to -125.6 dBm (-124 - 1.6 =
-125.6 dBm) as shown in Figures 2 and 3.
The 400 MHz desired IF signal is reported in Figure 3 (by marker 1) at a
level of -114.58 dBm.  Thus, the
signal to noise ratio (SNR) = -114.58 - (-125.6) = 11.02 dB SNR as is also
reported in Figure 2.

Another potential interfering signal is the third IM
(intermodulation) product (marker 2 in Figure 3) resulting from intermodulation
of the two interferers at the adjacent and alternate channels (markers 3 and 4
respectively).  However, this IM
interference (at 400.0001 MHz), falling near the middle of the IF band, is at a
low level of only -156.56 dBm or nearly 42 dB below the desired 400 MHz
signal.  Thus it is of little
consequence and can be ignored.

Figure 3, 400 MHz IF Spectrum with Interferers

Figure 3 shows signals emerging from the IF Filter.  All signals are perfectly without
noise.  The noise free signals of
Figure 3 are to be compared with Figure 7 which shows the signals and their
noise sidebands that are due entirely to LO phase noise.

Receiver Front End Analysis With LO Phase Noise

To demonstrate the role of LO phase noise in reciprocal
mixing (resulting in the degradation of apparent SNR), a model of an LO with
poor phase noise performance will be developed and applied in a LINC2 VSA
simulation similar to Figure 1 (except that phase noise will be added to the LO
represented by SIG2, ID=2 in the schematic).  The resulting spectrum around 400 MHz
will be observed and compared to Figure 3 to determine the effect of LO phase
noise on apparent SNR.

Consider the plots of LO phase noise versus frequency offset
in Figure 4.  The black trace
represents the phase noise measured from an actual LO.  The red plot is constructed such that it
has about 32 dB more phase noise at 10 KHz offset.  The Leeson SSB (single side-band) phase
noise model is then fitted to each curve as follows.

(Eq. 1) L(fm) = 10
Log[(1/2) ((f0/(2 Ql fm))^2 + 1) (fc/fm + 1) (F K T/Ps)], where fm is the
offset frequency (MHz), f0 is the LO frequency (MHz), Ql is the resonator
loaded Q, fc is the flicker corner frequency (MHz), F is the noise factor, K =
1.38 (10)^-23, T = 290 deg K, and Ps is the LO power in Watts.

Figure 4, LO Phase Noise vs. Frequency Offset (for two
different local oscillators)

Red curve (poor phase
noise):

Inserting into Eq. 1 the following, f0 = 1315 MHz, Ql =
4.38, fc = 0.002 MHz, F = 1.99, K = 1.38 (10)^-23, T = 290 deg K, and Ps =
0.00001 W gives:

(Eq. 2) L(fm) =
10 Log[((150/fm)^2 + 1)(1/(500 fm) + 1)(4 (10)^-16)]

Black curve (good
phase noise):

Inserting into Eq. 1 the following, f0 = 1315 MHz, Ql =
4.38, fc = 0.002 MHz, F = 1.26, K = 1.38 (10)^-23, T = 290 deg K, and Ps = 0.01
W yields:

(Eq. 3) L(fm) =
10 Log[((150/fm)^2 + 1)(1/(500 fm) + 1)(2.52 (10)^-19)]

Plotting Equations 2 and 3 and folding about the zero offset
axis yields the double side-band LO and phase noise plots of Figure 5.  Next a LINC2 VSA signal file
representing the LO from the red curve in Figure 5 was constructed.  This was done by sampling the value of
Eq. 2 at 1 KHz steps up to an offset of about +/- 200 KHz.

Figure 5, Double Side-Band LO Phase Noise Plots

The resulting LO phase noise file, LO1315Sig.dBm, is applied
to the LO source (Sig2, ID=2 in the schematic in Figure 1) by running a script
file.  The script editor (invoked by
selecting Edit/Run Script from the VSA schematic’s File menu) allows the
user to script a sequence of VSA simulation commands in any desired order.

In this case we use the following VSA script file to set up
a spectrum analysis accumulate (similar to a spectrum analyzer signal Max Hold)
function (Figure 6).  We follow this
command with a signal file sweep (SWP) command that applies the signal file to
the LO and sweeps the LO through each value, one at a time, while accumulating
the resulting signals that appear in the IF spectrum.  This ensures that each sampled value of
LO phase noise (as recorded in the file in 1 KHz steps) is applied and analyzed.

Figure 6, LINC2 VSA Script Editor

The result is the spectrum plot of Figure 7.  Signals identified by markers 1, 3 and 4
in Figure 7 are identical to signals marked 1, 3 and 4 in Figure 3.  These are the desired, adjacent channel
interference and second (alternate) channel interference respectively.  However, now we can clearly see the
phase noise spectra spread over the entire band and beyond.  The close in phase noise profile on the
alternate channel interferer (marker 4) looks just like the red LO phase noise
plot in Figure 5.  This phase noise
profile quickly changes, though, as we follow it to the right past the adjacent
channel interferer (marker 3 in Figure 7).
To the right of marker 3 the phase noise rapidly increases as the steep
slope of the filter’s lower skirt affords dramatically less attenuation
between 399.97 and 399.985 MHz.

Likewise, the adjacent channel interferer at marker 3 is
shrouded with phase noise, but only the left (lower) side looks like the red LO
phase noise profile of Figure 5.
Because the adjacent channel is so close to the filter’s lower
skirt the close in phase noise on this interferer does not appear symmetrical
about the signal.  Instead, this
interferer’s phase noise rises immediately to the right, surpassing the
phase noise levels of the alternate channel interfere at every point to the
right.  The relatively close
distance between the adjacent channel and the IF pass-band is the reason why
the phase noise from this interferer exhibits a pronounced negative slope
throughout the IF pass-band.

The important observation here is that the LO phase noise
translated to the adjacent channel interferer is, at all points throughout the
IF pass-band, stronger than the thermal noise floor as indicated by the
horizontal dotted line at -125.6 dBm in Figures 3 and 7 (the phase noise and
thermal noise being displayed per a 31 KHz integration bandwidth).  Though it has a negative slant, this
interferer’s phase noise exceeds the thermal noise floor by several dB on
average across the IF.  Thus the
effective signal-to-noise ratio (SNR) has been degraded by several dB when
compared to the no phase noise simulations of Figures 2 and 3.  This demonstrates the mechanism
(reciprocal mixing) by which LO phase noise can be transferred to strong
adjacent channel interferers and then spread out over the desired signal,
partially or completely masking the weak desired signal.  As can be seen in Figure 7, the desired
signal at marker 1 barely protrudes out of the phase noise in the IF band.

Figure 7, Spectrum Plot of Reciprocal Mixing into the IF
band

Figure 7 is to be directly compared to Figure 3 to see the
effects of phase noise, particularly the way it can rise up above the thermal noise
floor and mask the desired signal (marker 1) in the IF pass-band.

Improved LO Phase Noise is the Solution

One might propose that increasing the IF filter’s
rejection of the adjacent channel might help to reduce the in-band phase noise,
arguing that if the level of the interferer’s are reduced then their
phase noise will also be reduced.
However, this will not work because the phase noise has already been
added by reciprocal mixing ahead of the IF filter.  Increased adjacent channel rejection can
push the interferer down (as it passes through the IF filter) but it cannot
reduce the strength of the phase noise already in the IF pass-band.

We will now demonstrate that the effective way to reduce
in-band phase noise (due to reciprocal mixing) is to improve the phase noise
performance of the LO itself.  We
will create a new LO signal file that will follow the lower (grey) curve in
Figure 5 (black curve in Figure 4).
Using Eq. 3, we create the LO1315LowPhaseNoiseSig.dbm file (sampling in
1 KHz steps as before).

To run the simulation with the improved LO phase noise file,
the sweep command (SWP) in the script of Figure 6 is replaced with the
following (thus applying the new file):

SWP Sig2-1 File = C:\Program Files\LINC2VSA\
LO1315LowPhaseNoiseSig.dbm

Clicking Run in the Script Editor’s menu bar (Figure
6) runs the simulation.  When the
simulation has completed, the Accumulate Spectrum Graph automatically pops
up.  After applying the same span
and vertical axis limits (as in Figure 7) the improved spectrum of Figure 8
appears.  The simulation results of
Figure 8 show more than 30 dB improvement in in-band phase noise relative to
what was found in Figure 7.

Figure 8, Improved Reciprocal Mixing Performance in IF Spectrum
Resulting from Low Phase Noise LO

Conclusion

Comparing Figure 8 to Figure 7 demonstrates that for a given
offset, the in-band phase noise (due to reciprocal mixing) improves dB for dB
with the improvement in LO phase noise.
Whereas in Figure 7 (simulation with poor phase noise LO) the in-band
phase noise exceeded the thermal noise floor to become the limiting factor in
SNR, in Figure 8 the in-band phase noise is more than 20 dB below the noise
floor and therefore does not contribute to the SNR.

As a side note, we can look at the signals at Port2 in the
schematic of Figure 1 to see what the spectrum looks like before
filtering.  Figure 9 should be
compared to Figure 7 since they represent the phase noise spectra before and
after IF filtering respectively (when an LO with poor phase noise is
used).  Likewise, Figure 10 should
be compared to Figure 8 since these plots represent the phase noise spectra
before and after IF filtering respectively for a receive mixer employing a high
quality LO (low phase noise).

Notice in the comparison between Figures 9 and 7 or between
Figures 10 and 8 that the phase noise around the desired signal (in-band) does
not improve with IF filtering - only the interferers and their close in phase
noise are attenuated by the IF filter.
While the IF filter cannot reduce the in-band phase noise (only the
quality of the LO can), the IF filter is vital in reducing the strong
interfering signals in adjacent channels to levels below the desired in-band
signal.

Figure 9, Spectrum Showing Phase Noise from Reciprocal
Mixing Prior to IF Filtering (LO has High Phase
Noise)

Figure 10, Spectrum Showing Phase Noise
from Reciprocal Mixing Prior to IF Filtering (High Quality LO has Low Phase
Noise)

For system level simulation, the Visual System Architect
from ACS adds many built-in measurement functions for producing the
stage-by-stage cumulative system budget analyses that are essential to
successful system design, analysis, system performance verification, and report
generation. Full spectral domain analysis provides a spectrum analyzer view of
all signals and spurs at any point in the system.

At the circuit level, LINC2 provides high performance RF and
microwave design and simulation. In addition to schematic based circuit
simulation, optimization and statistical yield analysis, LINC2 Pro includes
many value-added features for automating design tasks, including circuit
synthesis.

More information about the ACS Visual System Architect and
LINC2 Pro can be found on the ACS web site at www.appliedmicrowave.com.

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