A Technique To Model A Frequency Mixer

A Technique to Model a Frequency
Mixer as a “Pseudo” Two-Port device.
(With application in Up/Down-Converter implementation)

Eric N. Oseassen
EL6010: Guided Studies in Electrical Engineering
Spring Semester - 2010
Long Island Graduate Center
Polytechnic Institute of New York University

Eric N. Oseassen Page 1 9/8/2010

Contents

I. Abstract.
II. Introduction.
III. Theory 1 – Ideal Commutator.
IV. Theory 2 – Mixer using Schottky diodes.
V. Theory 3 - Mixer as a Two Port device.
VI. Theory 4 - Mixer as a Linear device.
VII. Theory 5 - Characterizing a Mixer with S - parameters.
VIII. Implementation - Building & Simulating in Microwave Office.
IX. Summary – Uses and Applications.
X. Conclusion.


Abstract:

Mixers are three port, radio frequency devices, which utilize non-linear components to
multiply two, or more, incident signals. The products include sum and difference
frequencies of the input tones, and additional higher order terms. Due to the non-linear
nature of these devices, successful integration of mixers into a system typically requires
extensive computer modeling and a bit of trial and error at the bench. In this paper, a
method will be described which linearizes the modeling efforts and provides the designer
with an additional analysis tool.

Introduction:

Mixers come in a multitude of different architectures and topologies. This discussion will
focus on an implementation referred to as a Double Balanced Mixer (DBM)
incorporating a Schottky diode ring quad. The DBM generally offers high bandwidth,
superior harmonic suppression, and satisfactory power efficiency. These features
combined with a mature supply chain result in this variety being the core element of
many broadband microwave systems. As stated, this is not the only configuration which
will produce frequency translation; however, regardless of the particular design, the
techniques discussed in this paper will be applicable.

Fig. 1 - Schematic of a DBM with a diode ring quad.

One application which relies upon the frequency conversion (translation to another
frequency) property is known as a Down converter. Basically the Down converter is a
system block which conditions and converts, a received modulated radio signal, to a
lower intermediate frequency. The lower frequency will have the same information
content, or modulation as the high frequency RF signal, however it is now at a low
enough frequency where signal processing can extract out, or demodulate the desired
content.


Fig. 2 – Block diagram of Down converter.

Theory of Operation (I): Ideal Commutator.

As illustrated in Fig. 1, the 4 diodes are configured in such a way as to result in an LO
driven switch. Figures 3a and 3b below, demonstrate the operation (current flow) through
the IF port during alternate phases of the LO. When the LO is sufficiently positive, one-
half of the diode ring shorts, and the other half opens. The positive segment of the RF
balun* will have a ground return path through the tap on the LO balun. During the
negative LO cycle, the negative segment of the RF balun will flow through the other pair
of diodes, thus completing one full cycle of the LO switching action. The IF port is
basically sampling a portion of the RF signal during each half cycle of the LO wave. Due
to the characteristics of the RF balun, alternate current paths result in a phase inversion of
the sampled RF signal.

Fig. 3a – Mixer operation on LO positive cycle. Fig. 3b – Mixer operation on LO negative cycle.

* A balun is a type of transmission line transformer which converts a balanced (differential signal) into an
unbalanced (single ended signal); hence the term balun. It can also serve as an impedance transformer.


The previous discussion has focused on a qualitative observation of the component
actions. From a mathematical standpoint, the analysis becomes somewhat more complex.
For the sake of simplicity, it will be assumed that the LO switching function is an ideal
square wave.

Fig. 4 – Switching Waveform – Local Oscillator (LO).

As has been observed, the mixer is a “multiplication” circuit, therefore;

VLO t   VRF t   VIF t  . (Eqn: 1.0)

In this equation VLO (t) is defined as a square wave, VRF (t) is the modulated RF carrier
signal and VIF (t) is the product of the two. As a rule, square waves are expressed by their
Fourier series, therefore Eqn: 1.0 becomes:

  b  sinnt   V t   V t 
n RF IF (Eqn: 1.1)

Upon solving and plotting equation Eqn: 1.1 for some representative frequencies, the
graphs below were generated.

Fig. 5A – Illustration of phase inverted IF. Fig. 5B – Illustration of IF envelope.


Figure 5A illustrates the phase inversion of the sampled RF during one cycle of the LO.
Figure 5B shows the IF envelope as a product of “mixing” LO and RF signals. In practice
there are no ideal switches and generating a square wave at microwave frequencies is
problematic. The next section will review the issues of practical implementation.

Theory of Operation (II): Mixer using Schottky Diodes.

Most broadband Mixers utilize the Schottky diode as the switching element. The
frequency conversion is obtained by operating a diode with fast response and high cutoff
frequency as a switch, turning it on and off at a rate determined by the signal frequency of a
local oscillator (LO). As discussed, this commutating action produces signals at two new
frequencies.

The Schottky diode has been successfully modeled using the following equation:
  KT  Va  IRS  

q

I diode  I S e 

 1 (Eqn: 2.0)

 

Where:
 q = Electron charge; 1.60206 x 10-19 C.
 K = Boltzmann’s constant; 1.38044 x 10-23 J/K.
 T = Temperature in degrees Kelvin (K).
 Rs = Series resistance (Ω).
 Is = Saturation Current in Amps (A).

At room temperature (~ 296° K), the “q/KT” term reduces to a constant [1/ (0.026)] Volts.

The Schottky diode equation differs from a standard PN junction. The extra “IRs” in the
exponent results in a divergence from the ideal PN junction. However if we make some
reasonable approximations for initial conditions, an iterative solution can be plotted. It is
revealed that the “I x Rs” term becomes negligible within the desired range of operation.
This then leads to a simplified diode equation of the form:

Va 0.026v  
I diode  I S e (Eqn: 2.1)

 


Includes Rs

Fig. 6A – Schottky I-V curve theoretical.

In Figure 6A, we see the negligible difference between the simplified diode equation
(Eqn: 2.1) - (blue trace) versus the full Schottky equation (Eqn: 2.0) - (purple trace).


This in fact agrees favorably with real world measurements; Figure 6B is an I-V curve
plotted for a Watkins-Johnson Mixer implemented with a Schottky diode quad.

Watkins-Johnson Mixer: WJM4A
“Courtesy of Microwaves 101”

Fig. 6B – I-V curve of Physical Schottky diodes.

Figures 6A and 6B, illustrate the exponential nature of the Schottky diode, however it
also shows the deviation from an ideal switch. In Figure 7, the difference between an
“ideal” switch and a “Schottky” switch are highlighted.

Fig. 7 – Schottky diode response versus ideal switch

The analysis for the Schottky based switch differs somewhat from the analysis we used
for the “ideal commutator”. In order to illustrate some important properties that arise
from the exponential nature of the I-V curve, it is useful to expand and evaluate the diode
equation by means of a Taylor expansion.


Simplified Schottky Diode Equation:
Va 
I diode  I S e 0.026v 

 

Taylor Series expansion of an exponential function:
k 
Xk X2 X3
ex    1 X    Higher Order Terms
k  0 k! 2! 3!
Expanded Diode Equation:

I diode  I S
Va  Va  Va 
1
 1  0.026v  0.026v  0.026v
2 3

 Higher Order Terms}
1! 2! 3!

Where Va is the sum of the applied voltages, VLO and VRF. These signals are typically
sinusoidal in nature.

Therefore VLO  A cos LO t  and the unmodulated RF carrier, VRF  B cos RF t 

Substituting the terms for VLO and VRF into the Taylor expansion of the diode equation
yields the following:

  A cos LOt   B cos RF t    A cos LOt   B cos RF t  2  A cos LOt   B cos RF t  3 
Idiode I S  1      H .O.T 

  1!  2! 3! 


1 2 3 4

Reviewing this equation, we see that the first four terms of the expansion highlighted.
The first term results in a D.C. component and the second term is just a scaled version of
the input signals. The interesting part comes when we expand and evaluate the third and
fourth terms. For instance, the third term;

  A cos LOt   B cos RF t  2  A2 B2
  cos 2 LOt   cos 2 RF t   AB cos LOt  cos RF t 

 2! 
 2 2

Using trigonometric identities, this cascade can be further resolved.

cos 2  X  
 1  cos 2 X   cos  X   cos Y  
cos  X  Y   cos X  Y 
2 2

  A cos LOt   B cos RF t  2  A2
1  cos2LOt   B 1  cos2RF t    AB cosLO  RF  t  cosLO  RF  t 
2
   2 

 2! 
 4 4  

Sum & Difference Products

In the last term we finally capture the multiplication or “mixing” property of the Schottky
diode. The Sum and Difference products of the two input tones are apparent, and are in
fact the primary tones of interest in frequency conversion. It is also seen that 2nd
harmonic products of the LO and RF signals are generated.

The previous exercise illustrates the origin of various non-linear outputs
generated by driving an exponential device with a sinusoidal excitation.
The analysis applies only to a single diode, and is not meant to indicate
the content of a fully integrated double balanced mixer. Due to various
balun designs, diode barrier levels and termination topologies, it is
impossible to stipulate a response that applies to every DBM. Of interest
though, is that most available spur programs, base their calculations on a
Watkins-Johnson DBM, with a medium barrier diode ring quad, with RF
and LO signals travelling down wideband baluns. For a quantitative
analysis of spur levels, a designer must employ a non-linear simulator
such as AWR’s*, Microwave Office. It will be illustrated that for the
current application, this is not necessary.

Spurious Products

Performing similar trigonometric operations on the fourth term of the Taylor expansion
will yield higher order harmonics such as the third harmonic, but it will also produce
cross mixing products. These are referred to as M x N products, as in 2RF x LO, 2LO x
RF, 2LO x 2RF, and so on.
These spurious products, as they are called, are especially challenging to deal with at the
system level. Many are in-band or crossover the frequency band of operation. There are
two ways to work within the limits of these mixer spurs. For narrower band applications,
simulation tools exist which can show “clear areas” for a given a range of frequencies.

R = RF
L= LO

Fig. 8 – Mixer Web Chart: Hittite Microwave Mixer Spur Plot Program

The mixer web chart, plots a given range of LO and RF frequencies, and yields an IF
frequency window which will be clear of spurious interference. For broad band, multi-
GHz applications, this clear zone tool, becomes less effective, as there will always be
crossing, or near band spurs.

* AWR Corporation (Applied Wave Research) is an electronic design automation (EDA) software
company, founded by Dr. Joseph E. Pekarek

This is illustrated in Fig. 9 below. For swept RF and LO frequencies, maintained at a
fixed offset frequency, a fixed and constant IF frequency is produced at LO – RF.
However, we also see some higher order products, as shown.

The one of primary concern is the 2IF product, as it is proximal to the desired IF output;
but this is readily filterable. The other mixing terms crossover the RF and LO bands.
Visually these would seem to have no impact on the desired output. However they will
corrupt or interfere with the primary RF signal, thus degrading the dynamic range of a
system. A detailed discussion of the impact of spurs on system performance is beyond the
scope of this paper. However, it can be stated that a designer will characterize and model
his devices, and from there be able to determine what levels are acceptable for successful
operation.

Fig. 9 – Spur Table Fig. 9a – Spur Plots

Therefore the designer must make a compromise, he knows the spurs are there, but he
determines which level of suppression is sufficient for clear operation of his system.
Once spurs are acknowledged as a given or known quantity, they can essentially be
ignored. They are a tertiary product of device physics. So for a defined range of input
powers all M x N spurs will be at or below a certain level. The power threshold will
impact module or system level performance, but that has already been determined early
on in the design process as to what levels are acceptable.

Theory (III): Mixer as a Two Port device.

In Section I, it was demonstrated that a mixer can be described as a switch. Building
upon this idea, a DBM has been described as a DPDT switch (8) internally wired for
polarity-reversal. It has been shown that the LO functions only as a switch controller, i.e.,
just an external toggle and has only a secondary impact (LO leakage) at either the RF or
the IF ports (ports 1 &2 respectively). Pozar1 has demonstrated that a double balanced
mixer is very good at rejecting LO leakage to either the RF or IF ports. Therefore, taking
into account the inherent rejection of LO leakage and the fact that any residual LO at
these ports will not contain modulation; it is fair to say that a DBM is in fact only a two
port device.

Fig. 10 – Mixer as Two Port Device

Consider the ideal commutator, the combination of the diode ring and baluns can be
redrawn as a double pole double throw switch (DPDT) as shown in Figures 10, 10a, and
10b below.

Fig. 10 – DPDT Configuration
Fig. 10a & b – Alternate states.

During one half cycle (toggle) of the LO, a sample of the RF is directly transferred to the
IF ports; on the next LO half cycle the RF is sampled with a 180 degree phase inversion.
The result of this switching and inversion process was illustrated in figures 5a and 5b.

Theory (IV): Mixer as a Linear device.

Since a mixer can be successfully described as a switch, and based on our discounting of
secondary effects (LO leakage, reconverted reflections, etc.) and tertiary spur products; it
is fair to claim that, much as a switch, a mixer is a linear device. To confirm this claim, it
must be demonstrated that the Law of Superposition can be successfully applied. This
law states that a system is linear if, and only if the following is true:

 If Output “a” = f (a) and Output “b” = f (b)
Then…..
 Output (a+b) = Output (a) + Output (b)
Or….
 Output (a+b) = f (a+b) = f (a) +f (b)

Fig. 11 – Linear System


If we apply this test to a DBM, we see the following:

During the first LO half cycle; the RF is passed directly through to the IF ports by hard
wired connections, the Superposition test is clearly satisfied during this interval; two
points have been wired together. During the next LO half cycle the RF inputs are
swapped, and result in an inverted output. Mathematically this can be described by the
following:
 f a   a & f b  b
Apply Superposition test:
 is f a  b  f a   f b ?
Insert:
 f a  b  a   b  f a   f b : Confirmed

The above calculations demonstrate that the ideal commutating mixer passes the law of
superposition and meets the criteria to be called a linear device. As discussed a real mixer
produces undesired content, but in practice this content is filtered or otherwise suppressed.

Theory (V): Characterizing a Mixer with S - parameters.

So far it has been demonstrated that a Mixer can be described as a Linear, Two port
device. The external functionality of any linear, two-port network can be completely
described by means of an S parameter matrix. This leads to the concept of using S
parameters to model or describe a mixer.

Fig. 11 – S parameter illustration for two-port network.

Typically a Vector Network Analyzer (VNA) is the instrument of choice to measure S
parameters. Unfortunately, the VNA is not able to fully characterize a Mixer, owing to
the frequency translation property. In fact there is no single test-set which will
accommodate this characterization. However by using various test apparatus we can
construct the requisite file structure.

Fig. 12 – Mixer as two port device


A VNA produces four parameters for a typical two port device:

S11 corresponds to the RF port return loss
S21 is the through loss or “Conversion Loss”
S12 is the reverse isolation, or the leakage from the IF port back to the RF port.
S22 is the IF port return Loss

 Measuring S11

Measuring S11 is a relatively straightforward process; using a VNA, with a tracking LO
generator, a one port S parameter file can be extracted. It is critical that the Generator and
the VNA communicate via internal bus, so that a fixed frequency difference is maintained
between the two apparatus. The captured data is intended to correspond to the intended
operational state of the mixer as deployed in a system. Due to frequency dependent
parasitics within the device, operating a mixer at frequencies different than the intended
IF may result in invalid data.

The resulting data file will be in the form of: “file name.S1P”.

Fig. 13 – RF port Return Loss set-up.

 Measuring S21

Measuring S21 is somewhat more challenging. Since the mixer produces a “frequency
translated” output, we cannot use a VNA to directly capture S21 data. The approach here
is to use a Scalar Network Analyzer SNA). The SNA sweeps an RF signal at a user
defined power level; as with the VNA, the set-up requires a tracking LO generator.

Fig. 14 – Conversion Loss Set-up.

A scalar analyzer will display the power transfer function of the Mixer, versus the
injected RF frequency and power. Using a computer, and an Excel macro, this data can
be recorded: “file name: .xls.

This is where it gets a little tricky, the scalar analyzer only gives magnitude data; this is
because it exclusively measures referenced power. Therefore, unlike a VNA we will not
have any angle information. Capturing phase (or angle) turns out to be very challenging.

There is no direct way of measuring frequency translated phase (S21 angle). Yet in
principle, based on the definition of a mixer as a linear, two port device, there should
exist a means of deriving this information. Whenever a sinusoid is injected into a linear
device, a sinusoid must come out. The only things that can change between input and
output are the amplitude and the phase.

One approach is to measure Group Delay (GD), and derive phase information
accordingly. For example, define an input, sin ( t ), and an output sin (t   ) . The delay,
between the two signals, tp, is found by solving the following:
sin (t   ) = sin  (t  t p )
t   = t  t p
  =  t p )

t p 

d
GD is the derivative of radian phase with respect to radian frequency . Therefore phase is the
d
f2 d

f2
integral of GD: =
f1 d
d = 
f1
d =  f 2 -  f 1 =  f 2, f 1 .


Based on this description, measuring GD, in theory, allows the calculation of phase, and thus
construction an S21 angle plot.

In practice, this is not a trivial effort. A relatively straight forward technique to measure frequency
translated GD is described by Knox 11. His results demonstrate a relatively flat group delay across
the operating band of the mixer. This corresponds to an approximately linear phase response
frequency.

~ 135º

~ 45º

Measured delay linearity of a mixer as a function
of frequency. Knox 10

Fig. 14 – Frequency Translated Group Delay Fig. 15– Phase versus Frequency

Once this measurement is taken, our application would require integration over the individual
frequency points of interest (i.e. if we have a file with 201 points, a hundred integrations would
have to be performed). In addition, it is difficult to reconstruct an accurate wrapped phase response.
For instance, if we look at f1 and f2 in figure 15, we would calculate a  f 2, f 1 of approximately -
90°. This misses the entire the phase jump from +180° to -180°. A more accurate phase length
would be -90° - 360° = -450°

One last note on Group Delay; as was observed by Knox, GD tends to be relatively flat
over the operating band of a DBM; this translates into a linear phase versus  response.
Therefore if there are no rapid deviations from linearity in the thru phase this translates
into a component that has minimal perturbation on the transmitted signal (transfer
characteristic). In other words if a mixer has a 4dB conversion flatness, but a relatively
flat GD, the magnitude variations will overwhelm the minor contributions of GD.
Therefore, in this application an arbitrary number, from 0 degrees to 90 degrees, will be
assigned as angle.

 Measuring S12

Next we can measure S12 or IF to RF isolation. The approach would be similar to the set-
up described for measuring S11 (RF port return loss). In this measurement, the IF port is
injected with a swept RF frequency, and the output is measured at the RF port (i.e. S12).
This measurement will yield magnitude and phase data (an “.”S2P file). In practice, it is
not critical to measure S12 (IF to RF isolation). Typically, a well designed mixer will
have isolation greater than 15dB in this direction, and thus the impact of S12 on overall
mixer or module performance, will be negligible. In this regard the Mixer behaves like an


RF isolator; a relatively low loss forward characteristic and a high loss backward
characteristic.
I have stated that IF to RF isolation (S12) is of minimal concern in creating our model,
and for a first order approximation this is true. In other words, injecting an RF signal into
the IF port, and then measuring the leakage of this signal at the RF port will typically
yield a number greater than -15dB.

 Measuring S12 reconsidered:

There is one potential caveat to the claim that S12 has minimal impact on performance.
As noted the mixer translates frequency, this includes reflected signals. In figure 15
below, a mixer is shown terminated by source and load impedances at the RF and IF
ports respectively. A representative value for the return loss of these terminating loads is
10dB. The mismatch between the mixer ports and the loads will result in reflected signals.
These reflections have the potential to re-convert inside the mixer and cause degenerative
and regenerative phase and amplitude combinations.

Fig. 15 – Reflections & reconversions due to mismatch

For convenience, I have highlighted the primary signal paths. Signal 1 is the primary RF
signal incident upon the mixer, signal 2 is the down converted RF (the IF signal). Signal 3
is the IF signal reflected from the load mismatch back into the IF port. Signal 4 is the up
converted IF reflection (now at RF Frequencies) and signal 5 is the up converted IF signal,
now bounced back to the mixer due to mismatch at the source. If we attach power values to
these signals, we arrive at the following:

Signal 1: -20dBm (typical incident RF signal level)
Signal 2: -26dBm (assuming 6dB loss in down conversion mode)
Signal 3: -36dBm (assuming 10dB loss in the reflected IF signal)
Signal 4: -42dBm (assuming 6dB loss in up conversion mode)
Signal 5: -52dBm (assuming 10dB loss in the reflected RF signal and
re-incident at the RF port)

Comparing Signal 1 to Signal 4 a difference of 22dB is noted. Converting “dBm” to the
equivalent value in “Watts”, yields the following values:

Ex) -20dBm = 10(-20/10) = 0.01Watts = 10,000μW
Ex) -42dBm = 10(-42/10) = ………… = 63μW

If we consider the worst case scenarios, where the two signals add (0 degree phase
delta), or subtract (180 degree phase delta), we get -19.973dBm versus -
20.027dBm. It is clear that this level of perturbation will have almost no impact

upon the desired throughput. So the original claim that this reconverted reflection is
of minimal concern is valid.

In fact the same argument can be extended to M x N spur products, previously mentioned.
These are typically specified at 60dB below desired content. So instead of having
approximately a 20dB delta, we now have a 60dB delta. Their impact on ripple or
passband flatness is less by orders of magnitude and thus negligible.

 Measuring S22

In the application of this paper, the IF will be at a fixed frequency of 200MHz. To
measure the return loss of the IF port we revisit figure xx for S11. A new calibration will
have to be performed, with the VNA set at only one frequency (CW mode). At this point
a signal injected into the IF port at 200MHz will result in an *.*S1P file.

 Building the integrated S2P Touchstone(12) file
We now have enough information to start building our 2 port S parameter file.
The file structure that will be used is based on a Touchstone format*.

Fig. 16 – Touchstone file formats

The following are example headers:

1) # GHZ S MA R 50
2) # MHZ S DB
3) # HZ Z RI

MA, stands for magnitude and angle, whereas DB stands for decibel (20Log [Mag.]), and
RI represents Real and Imaginary (i.e. Polar Data).

For the current application, I will use DB as the default criteria, as it is easy to visually
recognize any inconsistencies with physical possibilities. The Touchstone file will have
the following form:

* A Touchstone file (also known as SnP file) is an ASCII text file used for documenting the n-port network
parameter data of an active or passive interconnect network.


Implementation: Building & Simulating in Microwave Office.

Fig. 17 – Constructed Touchstone file

Reading from left to right, we see the measured and approximated values tabulated into
their respective columns:

 S11 (RF port return loss): Measured “dB” and “angle”.
 S21 (Conversion Loss – dB only): Measured “dB”, stipulated “angle”.
 S12 (IF to RF port isolation): Measured “dB”, stipulated “angle”.
 S22 (IF port return loss): Stipulated “dB”, stipulated “angle”.

The S22 field has been entered as a stipulated value of -40dB. This is due to the fact that
all data fields must correspond to the swept RF frequencies. The measured S22 data will
be incorporated into our model as a separately.

S22, as measured and recorded by the manufacturer:

Fig. 17 – S22 (IF Return Loss – Vendor Data)


Conceptually we now have the following line-up:

S11 S12
RF Mapping S22 IF
S21 S22

Constructed Measured
S - parameter S1P - file
file

Fig. 18 – Two S parameter files

A full S2P file, versus RF frequencies has been constructed using measured and
stipulated data. A measured S1P file, at IF frequency, has been captured. Our goal is to
integrate the information with a mixer.

Using Microwave Office, we can import our two files, define a schematic window, and
pull the required S parameter blocks into the schematic. Finally we need to insert a Mixer
Model from the non-linear components section.

Fig. 19 – Constructed architecture

The ideal mixer will be modeled with 0dB conversion loss, as this is already accounted
for in our constructed file as S21. Since Return Loss has been measured for both the RF
and IF ports, we can enter near ideal numbers in the mixer model for these ports (i.e. Mag.
= 0.01 and Angle = 0°). Port to port isolation can be entered using vendor supplied data.
Finally, S22, or IF port return loss, is entered as a constant, since the current application
uses a fixed IF output frequency.

AWR: System Model for a Mixer (Closed Form)

Fig. 20 – Mixer Parameter File


The final schematic, as developed in Microwave Office is shown below. The constructed
S parameter file, and an ideal Mixer, are cascaded together.

Fig. 20 – Microwave Office Schematic

RF

Fig. 21 – S21 Response (Conversion Loss)


RF

Fig. 22 – S11 Response (RF Port Return Loss)

IF

Fig. 23 – S22 Response (IF Port Return Loss)


Summary: Uses and Applications.

The previous graphs illustrate that a DBM can be successfully described by a
combination of measured S parameters and an ideal Mixer model. The ideal Mixer model,
basically serves as a mathematical mapping function, translating the RF frequencies to a
lower, fixed IF frequency.

The significance of this effort is two fold. First, it allows a designer to model an entire
multi-component module in a simulator. In practical applications, the RF section of a
down converter may contain multiple gain blocks, switched filter banks, stepped
attenuator networks, and other components. The IF path, after the mixer, will likely
include an equal or greater number of signal conditioning components. When cascading
this many elements, it becomes very challenging to maintain all parameters within
customer specifications. Gain and gain flatness are two items that this technique is readily
applied to.

For the sake of simplicity, we have made some assumptions about group delay, and other
secondary functions of a mixer. To understand gross or large scale performance, these
assumptions were acceptable. Harmonic balance simulations are very good at
characterizing spurious or other non-linear impacts. However, when you are integrating
vendor supplied components into a system, you may not have insight into what internal
components have been used. Therefore you cannot adequately model these devices. This
technique allows a device to be characterized at the bench and then inserted back into a
computer model.

A second, more subtle, application zooms in on the mixer and its terminating components.
In practice, pass band ripple can also be critical to the end user, as rapid perturbations in
the RF envelope may distort modulated information. Accounting for these parameters is
challenging, however if we have a well defined S parameter block representing our mixer,
we can then select the input and output devices to determine their impact. Terminating
the IF path, with an attenuator, an isolator, a narrow band filter, etc., now becomes an
exercise in downloading manufacturer data for these components and swapping them in
or out of our model. In fact, combining this technique with a full harmonic balance in
Microwave Office will yield a very comprehensive analysis of system performance,
before anything is actually built. Previously these parts would have to be procured, and
physical installed into a system to gauge their impact.

In Conclusion.

In conclusion, a technique has been described which allows a mixer to be characterized
by means of S parameters. Applications have been discussed which show the usefulness
of this approach.


References

1) “Nonlinear Microwave and RF Circuits”, Stephen A. Maas, Second Edition,
Artech House, p.345-348.
2) “Mixers: Part 1 – Characteristics and Performance”, Bert C. Henderson, WJ Tech-
note.
3) “Mixers: Part 2 – Theory and technology”, Bert C. Henderson, WJ Tech-note.
4) “Mixers in Microwave Systems (Part 1)”, Bert C. Henderson, WJ Tech-note.
5) “Mixers in Microwave Systems (Part 2)”, Bert C. Henderson, WJ Tech-note.
6) “Mixer Basics Primer”, Ferenc Marki & Christopher Marki PhD, Marki
Microwave.
7) “Mixers”, Liam Devlin, Plextek Communications Technology Consultants.
8) “Mixer Linearity”, Glenn Dixon, http://znradio.com/
9) “Mixers”, Liam Devlin, Plextek Communications Technology Consultants.
10) “A Novel Technique For Characterizing The Absolute Group Delay Linearity Of
Frequency Translation Devices”, Michael E. Knox, Hewlett-Packard Company.
11) “Group Delay”, Ron Hranac, Cisco Systems.
12) “Touchstone File Format Specification (Version 2.0)” IBIS Open Forum 4/24/09.


Appendix

Calculated values for Schottky diode versus Standard diode.

.


A Technique To Model A Frequency Mixer

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