An Introduction to Passive I/Q, Single Sideband and Image Reject Mixers

In the realm of RF and microwave circuits, the I/Q mixer architecture is among the most intricate, complex and useful constructions RF engineers have devised in analog hardware. In the early 1900s, noted communication theorist John Carson performed the calculations that led him to conclude that amplitude modulated waves consist of two redundant sidebands. Eleven years later electronics researcher Ralph V.L. Hartley patented the essential structure that remains the basis for these types of modulators today.¹ Numerous applications have utilized the basic Hartley architecture since then, ranging from image rejection down-conversion for improved noise performance to single sideband up-conversion for simplified filtering, to I/Q modulation for complex wireless digital transmissions. Consisting of a delicate manipulation and recombination of in-phase, out-of-phase and quadrature-phased signals, the I/Q mixer architecture can be easily represented in a circuit diagram but is extremely difficult to realize in a physical layout. Creating compact I/Q structures with high performance over a broad bandwidth is a challenging task that remains the subject of ongoing research and development.

In this article, we answer the most common questions about I/Q, single sideband (SSB) and image reject (IR) mixers. We describe what each of these mixers does, how the passive implementations are constructed, common applications and considerations for each. We reference basic characteristics of double balanced mixers and quadrature hybrids used to construct these devices from Marki tutorials “Mixer Basics Primer”² and “Power Dividers and Couplers Primer.”³

What does an I/Q-SSB-IR mixer do?

Single Sideband Up-Conversion

As discussed in the “Mixer Basics Primer,” a normal mixer converts a given input signal at f_in to two signals at f_out = f_LO ± f_in (see Figure 1). One of these signals (called “sidebands” for the way they appear on each side of the LO on a spectrum analyzer) is at the desired frequency, and the other “undesired sideband” is filtered out to prevent signal transmission in adjacent channels. An ideal single sideband mixer translates the input signal to just one single frequency, at f_LO - f_in or f_LO + f_in, eliminating the requirement to filter out the undesired sideband.

Image Reject Down-Conversion

Conversely, the output of a normal mixer at f_out consists of two signals f_in = f_LO ± f_out, meaning that both the signal at f_LO - f_out and f_LO + f_out are converted to the same output frequency. Generally one of these is the desired signal, and the other is the undesired “image” that must be filtered out before the conversion. Therefore an ideal image reject mixer (IR mixer) converts only one sideband and eliminates the image signal without an image filter before the conversion (see Figure 2).

I/Q Signal Transmission

The function of an I/Q mixer is more difficult to describe. It can be shown either mathematically or experimentally that if both sidebands are transmitted to the receiver side of a normal mixer, a phase-locked LO is required to demodulate the incoming signal. If the LO used is 90 degrees out-of-phase (in “quadrature”) with the transmitted LO, the two sidebands cancel each other and no signal is seen due to the way each sideband inherits phase from the LO (see Figure 3).

I/Q mixers use this phenomenon to transmit two channels of data, one in-phase (I) and one with quadrature-phase (Q), without filtering out either sideband. As you can see in Figure 3, the I channel is modulated and demodulated with the same in-phase LO, while the Q channel is modulated and demodulated with the same LO 90 degrees out-of-phase.

What is the difference between I/Q, SSB and IR mixers/modulators?

Passive SSB and IR mixers are identical, but SSB mixers are used for up-conversion while IR mixers are used for down-conversion. While every passive SSB/IR mixer contains the structure of an I/Q mixer (as shown in the next section), they are used for different applications. An I/Q modulation always creates a double sided signal, and an I/Q demodulation always down-converts both sidebands. The term “modulator” generally refers to a device with an integrated LO amplifier or even an LO signal generator, while a “mixer” is always without the LO signal generation. Sometimes I/Q mixers or modulators are advertised as image reject mixers, with the expectation that the user will supply the IF quadrature combiner.

How does an I/Q-SSB-IR mixer do it?

Using phased power splitters and combiners to cancel undesired products is a common practice throughout microwave, RF and even optical engineering. A double balanced mixer uses a balun and a magic tee to cancel LO feedthrough and spurious mixing products. A triple balanced mixer essentially uses two double balanced mixers driven in a push-pull configuration to provide for overlapping LO, RF and IF frequency bands.²

I/Q, SSB and IR mixers extend the vectorial cancellation concept using 90 degree phase shifts in addition to the 180 degree phase shifts in the balanced mixers. Two identical signals that are 180 degrees out-of-phase with each other will cancel when combined together, leading to isolations and spurious cancellation in mixers.
I/Q-SSB-IR mixers use clever combinations of 90 degree phase shifts, applied differently to the different sidebands, to create cancellation of unwanted components.

The simplest way to understand an I/Q mixer is to imagine a mixer as performing a simple signal multiplication to the two inputs (see Figure 4). In this case a signal that is multiplied by an in-phase LO at the transmitter appears undistorted after multiplication by an in-phase LO and lowpass filtering at the receiver, but it is not present if it is multiplied by an out-of-phase LO. The implementation used in Marki I/Q mixers is shown in Figure 5.

Another way to understand I/Q mixers is to assume a sinusoidal input signal at the IF instead of an arbitrary time dependent function. This is useful for understanding SSB-IR mixers. In an I/Q up-conversion, the out-of-phase LO causes the upper sideband to be 90 degrees out-of-phase and the lower sideband to be -90 degrees out-of-phase with the input signal. At the receiver side, an in-phase LO converts them as is, leading to cancellation since they are 180 degrees out-of-phase with each other. A quadrature LO causes them to rotate back into place, adding constructively. You can see now that since the two sidebands have a phase difference of 180 degrees, we can eliminate one without eliminating the other by rotating both sidebands by either 90 degrees or -90 degrees and adding them back to an un-rotated copy of themselves (that is, one converted by an in-phase LO). Indeed this is the function that the IF hybrid in an SSB-IR mixer performs.

This additional quadrature hybrid placed between the I and Q ports introduces a second 90 degree phase shift to one signal, then recombines the identical, out-of-phase copies. After the additional phase rotation, one sideband is 180 degrees out-of-phase while the other is in-phase, causing one set of sidebands to add constructively and the other set of sidebands to add destructively.

The deceptively simple block diagram form of these structures masks a deep complexity intrinsic to their component elements. Let’s consider each component in turn, focusing on the miniaturized, integrated, planar and multi-octave form of these circuits (see Table 1):

RF In-Phase Power Divider:This is certainly the simplest component in the structure. I/Q mixer operation requires excellent phase match and low loss across the RF operating band, and isolation is desirable to reduce spurious products. A resistive power divider is possible but has higher loss than a reactive tee. The obvious solution, however, is the Wilkinson power divider, which provides low loss, phase matching and isolation, although it requires resistors and quarter-wave transmission lines that can contribute to a larger required circuit area.

Matched Mixers:Options for mixers are abundant (single diode, balanced FET, Gilbert Cell, triple balanced, etc.), but for most microwave applications the obvious choice is the double balanced diode mixer. This mixer can be planarized, offers good isolation and spurious rejection, high P_1dB, excellent repeatability of phase delay and amplitude balance and single ended operation on all three ports. One downside is that its frequency range is limited by the magic tee structure on its IF port, but this is usually not the main frequency limitation in the I/Q-SSB-IR mixer structure.

LO Quadrature Hybrid:This is where things go from tough to ridiculous in terms of integration. Making multi-octave Wilkinson power dividers is possible with microstrip circuits, and the multioctave baluns necessary for double balanced mixers have been achieved in a planar form in MMICs and to a greater extent in the Microlithic^® platform.⁴ A quadrature hybrid (essentially a 3 dB directional coupler with 90 degree phasing) is more difficult to realize, particularly beyond an octave bandwidth. This has only been achieved in the Microlithic platform. Most available surface-mount quadrature hybrids are narrowband, designed for balanced amplifiers. However, there are many legitimate ways to perform this quadrature signal generation, and we expect to see more of them implemented at microwave frequencies in the future.

IF Quadrature Hybrid:This is where integration goes from ridiculous to impossible. The IF is at a lower frequency than the LO, which means that a quarter wavelength is significantly longer. This makes implementation of a stripline quadrature hybrid more difficult, and generally engineers use magnetic assistance in these situations. Ferrites or absorbers cannot be integrated into a planar structure, however, so a passive
SSB-IR structure generally requires an external IF hybrid. The preferred solution to this problem is to connect the I and Q ports directly to a high speed digital-to-analog converter (DAC) that implements the quadrature phase shift digitally. This also allows for calibration to compensate for imbalance in the I/Q structure.

when to use an I/Q-SSB-IR mixer

The fundamental challenge of up-conversion is the translation of an input low frequency signal to a distortion free higher frequency output with high power, and the fundamental challenge of down-conversion is the translation of a high frequency signal to a lower frequency output with maximum dynamic range. The problem here is that mixers (and sometimes amplifiers) generate spurious products which need to be removed, necessitating a heterodyne or superheterodyne architecture with an intermediate frequency high enough so that the undesired image or sideband signal can be adequately filtered out without heavily attenuating the desired signal. An SSB-IR transmission system eliminates this filtering requirement by canceling out the image/sideband signal with balance, eliminating the need for filters that tend to be large and expensive. For IF frequencies much lower than the LO frequency, the two output sidebands will be too close together to filter, requiring
SSB-IR mixers. An IR mixer also improves the noise figure of the system by 3 dB by eliminating the sideband noise.

Do not be fooled into thinking that the SSB-IR is a panacea, however (see Figure 6). In a single sideband up-conversion the SSB mixer does not improve LO-RF isolation and the 2IF × 1 LO spur is only suppressed by an additional 3 dBc due to the RF power split.5 Since the LO feedthrough and the 2IF × 1 LO spur are both separated from the desired sideband by fIF, there are two spurs closer to the desired sideband signal than the undesired sideband, which is separated by 2·fIF. If more spurious rejection is required than that provided by LO isolation, then a heterodyne structure is required. Similarly the 2 RF × 2 LO spur is not suppressed by the image reject mixer. This requires a lowpass filter to remove it, limiting the dynamic range of very low IF systems. Finally, the image or undesired sideband is only suppressed by 20 to 50 dB (more for narrowband, low frequency systems and less for wideband systems). This is limited by the amplitude and phase balance of the mixer, which varies over frequency, temperature and time. Regardless, IR/SSB mixers are important for applications such as Doppler weather radar and quantum computing, which use low IF frequencies and have reasonable dynamic range requirements.

An I/Q transmission system addresses the problem of spurious and image products in a different way. Since it uses both sidebands to modulate the RF signal, there is no requirement to filter out the image or undesired sideband. The main limitation of this system is that the I channel will leak into the Q output and vice versa, limiting the dynamic range to this suppression ratio which is related to the sideband suppression ratio. This suppression is typically much less than the spurious, multitone intermodulation, or any other noise source, so spurs are not a meaningful problem. Similarly some unsuppressed carrier feedthrough is necessary to lock the receiver LO to the transmitted LO, meaning that LO-RF suppression is not as important. All of this limits dynamic range, but for the vast majority of communications systems the cost savings from the elimination of filters and additional conversion steps significantly outweighs the dynamic range limitation that the I/Q mixer imposes on the system (particularly after compensation). That is why every major modern communication system, including all cell phone and Wi-Fi standards, use some variation of advanced I/Q modulation such as QAM, QPSK or OFDM.

What can I do with an I/Q-SSB-IR?

The most obvious application of an I/Q mixer is communications. However, there are many other niche applications for these products, including:

Synthesizers/Pulse/Signal Generators:A single sideband mixer can be combined with a fixed high frequency LO and a tunable low frequency signal generator to create an easy-to-use synthesizer/high frequency arbitrary waveform generator (AWG). This is especially true if you have a dual channel DAC that supports this application.

Wideband Scanners:This is the opposite application of the synthesizer. Both high performance synthesizers and scanners typically employ multiple conversion stages with switched filter banks and complicated frequency plans. Less demanding applications with lower dynamic range requirements can use a single image reject mixer to scan across the entire RF/LO bandwidth of the mixer, which is as wide as 2 to 18 GHz in the case of the Microlithic.

Phase Detectors:As mentioned, I/Q mixers are frequently used for communications applications as phase modulators (QPSK, for example). Double balanced mixers are frequently used as phase detectors in phase-locked loops due to their ability to generate an error signal that can keep two signals in quadrature. They provide incomplete information, however, since a given voltage output can correspond to two different phase values, and this varies with input power. However, these ambiguities can be resolved with an I/Q mixer. The two output signals can be used to determine both the incoming signal amplitude and unique phase (see Figure 7).

Optical Transmission Systems:In many ways, an optical transmission network is an ideal transmission medium for an I/Q system. Since stray light does not couple into a fiber optic system, the only impairments come from the signals themselves. This is the ideal situation for an I/Q mixer, since noise filtering for stray signals is unnecessary (some filtering is usually employed for self-generated and amplifier noise). This means that twice the data rate can be provided in the same bandwidth that would be required for a double sided transmission. This is one of many reasons that I/Q data transmission schemes are being employed for high data rate optical communication systems.

What is the future of I/Q mixers?

In almost all situations, the main limitation of I/Q architectures is the ability to produce well matched quadrature-phased signals over very large bandwidths. Therefore, future I/Q mixers will require advancement in quadrature signal generation. As digital signal generation becomes practical at higher frequencies, we expect to see more circuits that combine the best of these digital circuits (excellent phase and amplitude balance with digital compensation) with the best of passive analog circuits (high power handling and single ended operation). Already the IF hybrid is largely eliminated as a result of high speed analog-to-digital converters (ADC) and DACs, and there is no indication that these are at the end of the line.

The dream I/Q mixer of the future will have amazing image rejection across a massive bandwidth, with incredible spurious rejection, linearity and power handling, all in one tiny package

1. R. V. L. Hartley, “Modulation System,” Patent No. 1,666,206, April 17, 1928.
2. F. Marki and C.  Marki, “Mixer Basics Primer - A Tutorial for RF & Microwave Mixers,” www.markimicrowave.com/Assets/appnotes/mixer_basics_primer.pdf, 2010.
3. Marki Microwave, “Microwave Power Dividers and Couplers Tutorial - Overview and Definition of Terms,” www.markimicrowave.com/Assets/appnotes/microwave_power_dividers_and_couplers_primer.pdf.
4. Marki Microwave, www.markimicrowave.com/2770/Mixers.aspx?ShowTab=113.
5. B.C. Henderson and J.A. Cook, “Image-Reject and Single-Sideband Mixers,” WJ Communications, Vol. 12, No. 3, May/June 1985.