Using the LINC2 Visual System Architect to Determine the System Spurious-Free
Dynamic Range
(SFDR)

Figure 1, Selecting the Visual System Architect
from the LINC2 Tools Menu

The concept of Spurious-free
Dynamic Range
(SFDR) provides an indication of the range of signal amplitudes that a radio
receiver can process.  The ability
of a receiver system to process the desired signal information is impaired if
the signal is in the presence of spurious interfering signals (spurs) or buried
in the noise.  The useful signal
level is limited at the low end by noise and at the high end by distortion
products (spurs created by the non-linear characteristics of the receiver).   The need for the desired signal to be
above the noise by a certain amount for a practical detector to process the
signal will be addressed later by employing a SFDR offset in dB equal to the
required detector threshold.  The
offset value will be used to calculate the effective SFDR based on the
receiver’s minimum detectable signal (MDS).  For simplicity in demonstrating the
concepts, it will initially be assumed that the MDS for the system is equal to
the noise level.

Therefore, the range of signals that can be processed most
effectively is one in which the signal is at least as strong as the
interference from noise but not so strong as to produce intermodulation
(IM) spurs that are stronger than the noise level.  (It is of no concern if the spurs are
below the noise level since they would be masked by the noise anyway).  The SFDR referred to here is the third
order spurious-free dynamic range.
This is the most common usage since the third order IM spurs are the
ones that are of most concern (because it is usually impossible to remove them
by filtering).

The concept of SFDR will be applied in this article to a
receiver circuit.  The concept and
supporting measurements used here could apply to other circuits as well, but
the application to receiver circuits is common.  The LINC2 Visual System Architect
software (VSA) from ACS (Applied Computational Sciences, Escondido,
CA) will be used to demonstrate the concept
and measurement of Spurious-free
Dynamic Range
for a typical radio receiver.

The LINC2 VSA program (Figure 1) offers at least two
different ways to determine the SFDR, direct simulated SFDR measurement and
calculated SFDR via system cascade budget analysis.  Both methods will be presented in the
following paragraphs.  First, the
VSA’s Spectral Analysis capability will be used to display all the
signals, IM spurs and noise spectra necessary to directly measure the
SFDR.  Employing the VSA spectral
analysis method has the advantage that it visually applies the concept of SFDR
in an intuitive manner that is analogous to real world instruments (i.e. a
spectrum analyzer) making the same measurement.  Then, finally, the VSA’s Cascade
Budget Analysis method will be used to arrive at the same value for the system
SFDR.  While cascade budget analysis
does not provide as much insight into the concept of SFDR (by simply reporting its
value), it does provide additional valuable information on how the system
design affects the SFDR.  In
particular, the SFDR budget analysis will show graphically how the inclusion of
filter components contributes directly to improving the system SFDR.

Using
the Visual System Architect’s Spectral Domain Analysis to Measure SFDR

The LINC2 VSA Spectrum Analysis plots will be used to find
the SFDR for the receiver circuit in Figure 2.  The lowest signal level (at the input
from the antenna terminal) will be found that generates an output signal at the
detector (Port 1, Output) that is just at the noise level.  The input signal level will then be
increased until IM3 products appear at this same noise level at the output
port.  The difference between these
two levels is the SFDR.  The SFDR
found by VSA spectrum analysis will then be compared to other methods [1].

Figure 2, LINC2 VSA Receiver Schematic for SFDR analysis

With the receiver circuit schematic entered as in Figure 2,
clicking Analyze and View > Plot yields a view of the
output spectrum as shown in Figure 3.

Figure 3, VSA IF Output Spectrum at the Noise Level (for
Input Signal Levels of -121 dBm)

We note that an input signal level of -121 dBm (at the antenna input terminal in Figure 2) puts the
two output (fundamental) tones just at the noise level of -87.2 dBm (as shown in Figure 3).  We denote this input level as SFDR_Sig_Pwr_In1 = -121 dBm.

The antenna input signal level that caused the output in Figure
3 to coincide with the noise level was predetermined by simultaneously
adjusting the two fundamental tones (at 500.01 and 500.02 MHz) until the corresponding
receiver signal outputs were equal to the noise output level (dashed line
labeled Noise in Figure 3).

The horizontal dashed line representing the noise floor in
Figure 3 is a function of the system Noise Bandwidth which was set at 100 KHz
via the Set > Simulation Control
menu (Noise).  Since there are no filters in the
schematic (Figure 2) the noise bandwidth setting of 100 KHz represents the
detector bandwidth.  In this case
the detector bandwidth is the limiting factor for determining system noise
bandwidth.  In the next section the
same noise bandwidth will be explicitly enforced by the addition of an ideal
100 KHz IF filter.

The next step is to find the input level that produces two
IM3 spurs with levels equal to the noise floor as shown in Figure 4.  Note that this time it is the IM3 spurs
(markers 3 and 4 in Figure 4) that are set equal to the noise floor (by
appropriately adjusting the level of the antenna input signals).  This results in the two fundamental output
tones (markers 1 and 2) increasing to nearly 70 dB above the noise.  As before, we check the level of the
input signals and find that they are both at -51.06 dBm.  We denote this input level as SFDR_Sig_Pwr_In2 = -51.06 dBm.  The
input SFDR is therefore:

Input SFDR = SFDR_Sig_Pwr_In2 - SFDR_Sig_Pwr_In1 = (-51.06) -
(-121) = 69.94 dB ß

We can also find the SFDR from the difference between the
fundamental output levels from Figures 3 and 4 as follows:

Output SFDR = (Marker 1, Fig. 4) - (Marker 1, Fig. 3) =
(-17.28) - (-87.21) = 69.93 dB ß

Figure 4, VSA IF Output Spectrum with Input Signal Levels
set at -51.06 dBm

The input and output SFDR are virtually identical as would
be expected from measurements made in the linear portion of the system’s
gain curve where a difference in two input levels yields the same difference
between the corresponding output levels.
In this case we simply report the system SFDR = 69.94 dBm ß
relative to the input.

Using
the LINC2 VSA’s Cascade Budget Analysis to Plot the Cumulative SFDR through
the System Cascade

The following is an alternative method of determining the
SFDR based on the system IIP3 (input third order intercept point) and the
relation SFDR = (2/3)*(IIP3 - Pn), where Pn is the noise floor relative to the input (Pn = 10*Log(KTBF)).  Both IIP3 and Pn
are expressed in dBm.

It was mentioned earlier that the noise floor (and thus the
SFDR) is a function of the system Noise Bandwidth which was set at 100 KHz in
the previous analysis via the Set >
Simulation Control menu.  The
receiver system schematic in Figure 2 has no explicit frequency selective
devices and therefore all the simulations up to this point have used this
global simulation noise bandwidth (BW) setting of 100 KHz.

Form this point forward we will use an ideal 100 KHz IF
filter in the schematic (FLT1 in Figure 6) to explicitly define the system
noise bandwidth.  To demonstrate the
fact that we will now use the IF filter to define the noise bandwidth instead
of the global simulation BW, we set the System
Noise Bandwidth via the Set >
Simulation Control menu (Figure 5) to 1.5 GHz.  The simulator will then use the global
noise BW (in all parts of the circuit where there is no defined BW) from the
input port to the IF filter, and use the 100 KHz IF filter bandwidth from there
on to the output port.

The arbitrarily
large setting (1.5 GHz) for the global NBW specified in Figure 5 will be in
effect until the first circuit component is encountered that has a narrower
noise bandwidth (at this point the narrower NBW applies).

Figure 5, VSA Noise Simulation Control (Global System
Temperature and Noise BW Setting)

Figure 6, Using an IF Filter to Control Noise Bandwidth in
the LINC2 VSA System Simulation

The schematic in Figure 6 has two things that are different
than the schematic in Figure 2.  In
addition to the IF filter already mentioned, Figure 6 uses a different mixer
model.  This is to demonstrate that
the SFDR measurement is not sensitive to the type of mixer model used as long
as we can specify the mixer’s gain, IIP3, and NF in the model.  All of the LINC2 VSA mixer models allow
for the specification of these three parameters, so any one of the several VSA
mixer models can be used to model the system SFDR.

We will not use VSA Spectrum Analysis to manually measure
the system SFDR this time.  Instead,
we will use the SFDR measurement that is already a part of the built-in functions
in the Set > Output menu as shown
in Figure 7.

Figure 7, Adding Measurements to the LINC2 VSA Cascade
Budget Analysis

Before running the simulation on the schematic of Figure 6,
we add Output Spurious-Free Dynamic
Range (SFDROut) to the
list of measurements.  Next, clicking
Analyze and View > Cascade Budget Analysis produces the plots shown in
Figure 8.  The bright blue plot at
the top of the stack of curves in Figure 8 shows the SFDR at the output of each
stage in the cascade of system components.

We can immediately see the effect of the IF filter in the
jump in SFDR between the outputs of stages 6 (ATN3) and 7 (FLT1).  This improvement in SFDR is a result of
the narrowing of the system noise bandwidth through the IF filter (which
reduces the total noise power).  The
filter’s reduction of the noise power is also seen in the simultaneous
drop in total integrated noise power (Noise PWR curve near the bottom of the
graph).

Figure 8, LINC2 VSA Cascade Budget Analysis

The VSA simulation can produce numerical tables of values
for all of these plots by selecting Save
Output… from the Chain Analysis graph’s File menu.  The
numerical values for SFDR from Figure 8 are as follows:

Measurement   Type:  SFDROut

Stage               Parameter
Value         Units

0                      54.8097             dB

1                      45.2764             dB

2                      45.2309             dB

3                      44.0166             dB

4                      44.0102             dB

5                      42.9075             dB

6                      42.9035             dB

7                      70.7441             dB

8                      69.9253             dB
ß Final output
SFDR

The final output SFDR value of 69.925 dB compares very
favorably with the value (69.94 dB) obtain earlier by manual measurements taken
from the VSA Spectrum Analysis graph.
We can conclude that either method is an accurate way of determining the
system SFDR.

Figure 9, LINC2 VSA System Performance Analysis Reports

If we are only interested in the final system SFDR or other
total system parameters, we can simply select View > Reports after running a simulation (Analyze) to get the total system values as shown in Figure 9.

The values reported for the SFDR in Figures 8 and 9 do not
depend on the power levels of the signals at the input port (SIG1, ID=1) for
the schematic of Figure 6.  However,
the Signal-to-Noise Ratio (SNR) does depend on the power of the input signals.  Figure 9 reports a SNR for the combined
power of both fundamental signals.
Since the simulation of the Figure 6 schematic was run for input levels
very close to the high end of the input spurious-free dynamic range, the SNR
for one tone should be very close to the total SFDR value.  Taking the SNR value of 72.93 dB from
the table in Figure 9 and subtracting 3 dB we get 69.93 dB which agrees very
closely with the SFDR value of 69.925 dB from the same table.

It is implicit in the analyses previous presented that the
system can detect a signal with a power level equal to the noise floor.  In practical systems the detector will
need to be presented with a signal somewhat greater than the noise floor for
proper processing.  We can specify a
threshold or minimum power level above the noise that a signal must be at for
adequate processing.  This
specification reduces the effective SFDR by each dB that the signal is required
to be above the noise floor.  The
LINC2 VSA has provisions for entering this number as a SFDR offset when SFDR
measurements are included in the VSA’s Cascade Budget Analysis plots (as
shown in Figure 10).

Figure 10, Specifying a Detector Threshold as an SFDR
Offset Value

Figure 11 shows the SFDR plotted with and without a 6 dB
SFDR offset applied (dark blue and light blue plots respectively).  The plotted data is shown numerically in
the following table:

Measurement   Type:  SFDROut

Stage   Parameter Value         Units    6 dB Offset Value         Units

1          45.2764             dB        39.2764             dB

2          45.2309             dB        39.2309             dB

3          44.0166             dB        38.0166             dB

4          44.0102             dB        38.0102             dB

5          42.9075             dB        36.9075             dB

6          42.9035             dB        36.9035             dB

7          70.7441             dB        64.7441             dB

8          69.9253             dB        63.9253             dBß Final output
SFDR

Summary

Two methods of determining the SFDR for a receiver was
demonstrated.  First, LINC2 VSA
Spectrum Analysis was used for calculating the SFDR.  The Spectrum Analysis method yielded a
great deal of insight into the process but required a few steps to
complete.  It was then shown how the
LINC2 VSA can automate the SFDR measurement by using the SFDR measurement that
is already a part of the built-in functions in the Set > Output menu.

LINC2 is a high performance RF and microwave design and
simulation program from ACS.  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.

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

Figure 11, SFDR Plotted With and Without
a 6 dB Offset (Dark Curve has Offset Applied)

References

[1] The schematic of Figure 2 along with the subsequent
analysis results in Figure 9 closely follow Example 5.4 - Combined Parameters for a Standard Cascade in section
5.4 “OPTIMIZING CASCADES”
in the book “Practical RF System
Design” by William F. Egan, published 2003 by John
Wiley & Sons, ISBN: 0-471-20023-9.