VSS IQ Mixer Model

Introduction

The Virtual System Simulator (VSS), contained within the AWR Design Environment (AWRDE), does not currently contain a model for an IQ Mixer. However, using existing elements in VSS, a behavioral model for a IQ mixer can be constructed. This model can be constructed to incorporate noise, distortion and isolation impairments giving simulation results that match specified data. This article is intended to demonstrate the construction of an IQ mixer using base elements including the interpretation of data sheet specifications and how to apply these to parameters of the VSS elements.

IQ Mixer Background

IQ Mixers fall into two operation mode categories: down converter and up converter as shown here:

In the down converter, the signal at RF, s(t), is split into two channels. These channels, termed in-phase and quadrature-phase, are normally designed to be identical except for the phase of the LO signals being 90 degree offset from each other. The RF signal is mixed down to the I-port and Q-port baseband signals, i(t) and q(t). In the up converter, the two baseband signals at the I and Q ports are mixed up and combined to form the RF signal, s(t).

 Passive IQ Mixers can generally be used in either up or down conversion mode. Other toplologies may incorporate amplifiers, variable gain control and other elements that render these devices dedicated to either up or down conversion operation. In addition, the IQ mixer can be used in a variety of different applications as outlined below:

Single Sideband Mixer

One of the fundamental uses is that of a single sideband (SSB) mixer as shown here:

At the IF input, two identical signals separated by 90 degrees are presented to the I and Q input ports of the IQ mixer. An external 90-deg Hybrid coupler can be used to generate the two different I and Q port signals from a single input signal. Following the I path, the signal at the output of the I-path mixer is:

and at the output of the Q-path mixer,

Summing these signals, results in the output

The upper sideband does not exist, only the lower sideband is available at the output. By reversing the sign of one of the input signals would result in the upper sideband at the output and the lower sideband being suppressed.

Orthogonal Signal Transmission

 Another application is the simultaneous transmission of two signals as depicted in this diagram:

Independent signals at IF are presented to the I and Q path inputs. Due to the signals being orthogonal (90 degrees out of phase), they can both be transmitted in a single RF channel. Once down converted, the two signals can then be separated into their original representations. Without the property of orthogonality, the two signals could not be separated into their original representations.

 Complex Signal Transmission

A real signal has even magnitude symmetry about DC and odd phase symmetry about DC. However a complex signal does not necessarily need to obey the even and odd symmetry properties. A complex signal at baseband is shown in this example:

Usually digital signal processing (DSP) techniques are used to separate the complex modulated baseband signal into their real and imaginary parts. After upconversion through the IQ mixer, the signal at RF is the representation of the complex baseband signal.

Some more detail on how complex modulation works can be shown with this graphical representation of down conversion through and IQ mixer:

The yellow modulation shapes represent the signal at RF. Being a transmitted signal at RF, the signal must be real and real signals are mathematically represented with a mirror image in the negative frequency axis. The red shapes show the I path downconversion where the LO signal is a cosine. The RF signals in the positive and negative frequency ranges will both mix down to baseband and overlap. The blue shapes show the downconversion in the Q-path where the LO signal is a sine. Once digitized, DSP is used to add the I and Q path data together with Q-path data being modified by multiplying the data by -j (shifting the phase by -90 degrees). Two of the baseband components will cancel and two of them will add resulting in a complex baseband signal that represents the signal at RF.

Image Rejection

In all the use cases outlined above, one key performance criterion is image rejection. Ideally a sideband on one side of the LO should not show up as a sideband on the other side of the LO. For instance in the case of the single sideband mixer, using the diagram below, the sideband at a frequency of F_C + F_SIG is the desired signal and the undesired image is the signal at a frequency of F_C - F_SIG

Image rejection is the amplitude difference between the desired signal and its image. For a SSB application, the danger is that the image may fall into an unallowed transmission band. For digital modulation applications, orthogonality is no longer maintained, thus corrupting the signal and leading to potential bit errors.

Gain and phase imbalance between the I and Q channels is primarily responsible for generating the image signal. A model for the generation of the image response is shown here:

Gain offset is presented in one of the channel and phase offset is presented in one of the LO signals. After a generous amount of algebra, a closed form equation for image rejection as a function of both gain and phase imbalance is:

Plotting this equation results in this graph:

This result shows a remarkable sensitivity in both gain and phase imbalance on image rejection.

VSS Model Construction

Because signal flow in VSS is directional, separate models for the IQ Mixer need to be constructed for either down conversion mode or up conversion operating mode. An example project that demonstrates the VSS IQ Mixer models can be downloaded using these links:

IQ Mixer VSS Models.emp

IQ Mixer VSS Models.vin

Down Converter IQ Mixer

Shown below is the behavior VSS model for the down converter IQ Mixer:

The mixers use the MIXER_F element so that M,N spurs can be modeled. If M,N spur simulation is not a requirement then either MIXER_B or MIXER_B2 elements could be used instead. This document will show the use of MIXER_F, but many of the parameter settings for the other mixer elements will apply. The important mixer parameter unique to the down converter model is the MODE setting, it must be set to DIFF in the down converter case.

Amplitude imbalance is accounted for using the RFATTEN element in one of the I or Q paths. Nominally the attenuation value is 0 dB which represents no amplitude imbalance.  A 90-degree hybrid coupler (QHYB_12) is used to create LO signals to both mixers with a 90 degree phase separation. The PHSBAL parameter in the QHYB_12 model models the IQ mixer phase imbalance. Nominally this is 0 degrees representing no phase imbalance.

Up Converter IQ Mixer

Shown below is the behavior VSS model for the up converter IQ Mixer:

This is very similar to the down converter model with the exception that a COMBINER element is used at the output and the MODE parameter of the mixer elements is set to either SUM or DIFF. For RF Budget analysis of low side mixing, use DIFF and for analysis of high side mixing, use SUM. For time domain simulations, always use the SUM setting.

Setting Parameters

Applying datasheet specifications to the VSS model element parameter is dependent on the measurement conditions noted in the data sheet. Careful attention needs to be paid on how to interpret the data sheet values.  Different nomenclature is used amongst the various IQ mixer vendors for noting how the performance was measured. In some data sheets measurement conditions may vary depending on the performance specification.

Some passive IQ mixers may only specify that the device is measured as either an up or down converter. The assumption is that values measured in one mode of operation apply to the other mode of operation.

When the measurement conditions indicate that I and Q ports are combined with either a quadrature or 90 degree hybrid coupler, the measurement setup is as shown below for the case of an IQ down converter mixer:

If the indication is that the I and Q port powers are not combined, then the measurement is made from the RF port to either the I or Q port.

In the example project referenced above, a couple of testbench system diagrams with accompanying graphs/measurements are given. Here is a testbench system diagram for down converter mode measurements:

And here are some simulation results for operation in down converter mode:

Here is a testbench system diagram for up converter mode measurements:

And here are some simulation results for operation in down converter mode:

Gain

In the down converter mode of operation the gain at the output of the external quadrature hybrid coupler is 3 dB higher than the gain at either the I or Q output ports. If the datasheet gain is specified with an external hybrid coupler, then set the mixer gain to the datasheet value. If the datasheet gain is specified without an external hybrid coupler, then set the set the mixer gain 3 dB higher than the datasheet gain specification.

For instance in the above example, the mixer conversion gain is set to -10 dB. This would correspond to a datasheet gain specification of -10 dB if measured using an external hybrid coupler. This would also correspond to a datasheet gain specification of -13 dB if an external hybrid coupler is not used.

Noise Figure

For a passive IQ mixer, if not otherwise noted, the noise figure is the opposite sign of the conversion gain. In the above example, with a mixer conversion gain of -10 dB, the mixer noise figure parameter is set to +10 dB. This corresponds to a datasheet noise figure of 10 dB when measured with an external hybrid coupler or +13 dB if datasheet noise figure is specified without an external hybrid coupler.

IP3 and IP2

Most often IQ Mixer datasheets specify input IP3 and IP2. The mixer IP3TYP and IP2TYP should be set for input, not output. The mixer input IP3 and input IP2 parameters should be set to 3 dB lower than the datasheet specification. This takes into account the loss of the input splitter for the down converter. In the above example, the mixer input IP3 parameter value is +5 dBm, leading to a corresponding datasheet specification of +8 dBm.

P1 dBm

Input P1 dBm is normally specified in IQ mixer datasheets. For that reason, set the mixer P1DBTYP to Input P1dB. For similar reasons as in the case for IP3/IP2, set the mixer P1DB value 3 dB lower than the datasheet specification.

LO to IF Isolation

LO to IF isolation is most often specified without an external quadrature hybrid coupler. The mixer’s isolation value must be 3 dB less than the datasheet value to account for the loss through the IQ mixer’s LO hybrid splitter loss. Also which mixer parameter to set depends on whether up or down conversion operating mode is being used.

For down converter operation, if using MIXER_B/B2 use the LO2OUT parameter. For MIXER_F, use the LO=1, RF=0 value in the spur table data file as shown:

In this example, the datasheet LO to IF Isolation specification is 40 dB. The mixer’s setting is then 37 dB. For an LO Power of +15 dBm, the resulting LO feedthrough power at the I or Q port is then +15 dBm – 40 = -25 dBm:

For up converter operation, use the mixer’s LO2IN parameter. Again, set this value 3 dB less than the data sheet specification. Be mindful of the parameter’s sign: the LO2IN value must be negative. So for instance if the datasheet LO to IF isolation specification is 40 dB, then the LO2IN parameter value would be -37 dB.

LO to RF Isolation

For down converter operating mode, use the mixer’s LO2IN parameter for either MIXER_B/B2 or MIXER_F. Make the mixer parameter value 3 dB less than the datasheet specification. For instance if the datasheet LO to RF specification is 50 dB, then make the mixer’s LO2IN parameter -47 dB (keeping in mind that this parameter value must be negative).

For up converter operating mode, with MIXER_B/B2 use the mixer’s LO2OUT parameter. For MIXER_F, use the spur table’s LO=1, RF=0 value as shown:

In this example the datasheet LO to RF specification is 50 dB, so 47 would be entered into the spur table

Return Loss

Apply port return losses to the outward facing component in the IQ Mixer model. Highlighted are the port return loss parameters for the down converter model:

Input return loss is applied to the input splitter, LO return loss is applied to the LO’s hybrid combiner and output return loss is applied to the mixer’s SOUTMAG parameter. Be mindful of the conventions for each element: return loss in dB, VSWR, or reflection coefficient.

Highlighted here is the return loss parameters as applied to the up converter:

Image Rejection

As explained earlier, image rejection is largely a function of amplitude and phase imbalance between the I and Q paths of the IQ Mixer. The models in the example project provided have means of applying both amplitude and phase imbalance. Using the plot “Image Rejection vs. Gain and Phase Imbalance” in this article, one could set the amplitude and phase imbalance parameters for a desired image rejection value.

For instance, suppose one wants to model -35 dB of image rejection. One possibility is to choose the point shown here:

Then lookup the gain and phase imbalance that corresponds to the chosen point. In this example phase imbalance is 1 degree and amplitude imbalance is approximately 0.25 dB. Apply these values to the IQ mixer model as shown and the spectrum shows the image rejection:

Spurs

Mixer M,N spurious responses may take some experimentation to get the desired simulation performance. This is because the spur amplitude level is a function of both the spur’s RF multiplication value, M and the loss in front of the mixer. For example, in the downconverter mode the splitter loss is in front of the mixer, thus lowering the power presented to the mixer. Also how the manufacturer states the measurement conditions, whether or not an external quadrature hybrid coupler is used, can affect the spur level.

In this example the 2,-2 spur in down converter operating mode with RF input frequency of 1.2 GHz and an LO frequency of 1 GHz will appear at a frequency of 0.4 GHz. The spur table entry is 30 dB resulting in a simulation value of approximately -33 dBc:

Here, the 3 dB splitter loss affects the spur level.

Summary

This article explains the basics of applying datasheet specifications for an IQ Mixer to models that can be created for VSS simulations. There are IQ Mixers on the market that incorporate higher levels of integration including LO Multiplication, amplification, variable gain. Using the starting point explained in this article, the device dependent embellishments can be added to the models.