In high-speed wireless communications systems, signals must be translated in frequency by up-conversion or down-conversion for signal propagation and processing. Traditionally known as mixing, this frequency conversion is fundamental to both receive and transmit chains. 

Mixers and modulators, then, are the basic building blocks for radio-frequency (RF) systems. As wireless communications standards continue to evolve, it is essential to review the characteristics of these building blocks and to understand how mixers impact the overall system performance. 

In any radio design, mixers and modulators allow frequency translation and enable communication. They establish the basic specifications for the entire signal chain. And, they see the highest power in the receive chain, up-convert signals from the digital-to-analog converter (DAC) in the transmit path, and enable digital pre-distortion (DPD) systems, impacting the performance of the complete communication system.

So how does the basic mixer work, which specifications are important to consider, and what options of mixers and modulators are available today to improve and simplify system design?

Basic Mixer Operation
In its simplest form, the mixer is a multiplier. Where audio mixers only add signals, RF mixers actually multiply the input signals to produce output signals at new frequencies. RF modulators and demodulators are essentially mixers. These devices take a baseband input signal and output an RF modulated signal or vice versa.

We approach this article from the mixer perspective for most of the discussion because whatever impacts a mixer also impacts a modulator. Typically, the receiver uses down-conversion to enable the processing of high-frequency RF signals, and the transmitter converts lower-frequency baseband signals to high-speed radio frequencies. All of the mixer’s ports behave as both a load and a source.

In our first example, we use down-conversion. The two inputs are the RF and local oscillator (LO). The output is the intermediate frequency (IF). The output signal consists of both the sum and the difference of the inputs (Fig. 1). Mathematically, we can explain these mixing output components using Equations 1-3:

RF input = A1sin(ω1t + φ1) (1)
LO input = A2sin(ω2t + φ2) (2)
Output IF = A1A2sin(ω1t + φ1) sin(ω2t + φ2) (3)

Using trigonometry identities, we get an output comprising the sum and difference:

Output IF = (A1A2/2) \{cos\\[(ω1 + ω2)t +(φ1 + φ2)\\] + cos\\[(ω1 – ω2)t – (φ1 - φ2)\\]\} (4)

Depending on the IF frequency and system level planning, several down-conversion steps and filtering may be necessary to acquire the signal quality needed for signal processing. (LO > RF is high-side injection, and RF > LO is low-side injection.)

The mixer in the up-conversion process is usually employed early in the chain following the creation of the baseband signal. In this process, IF is now the input and RF is the output. Again, the output is the sum and difference of the input signals.

Additional filtering at the input and output is needed to attenuate the unwanted products for the desired performance similar to the receive chain.

Conversion Gain
Conversion gain is the staple benchmark for mixers to verify functionality in production. This is the ratio of the output signal level to the input, and normally it is expressed in dB. Conversion loss for passive mixers typically is indicated as insertion loss.

The minimum loss is calculated using the ratio of the RFOut current (g1vrf/2 = gonvrf/π) and IFOut current (g1vrf = gonvrf/2). The ratio becomes 2/π and, thus, the conversion gain is (2/π)2 or –3.92 dB, assuming all impedances are equal and the LO input is a square wave.

If we consider a continuous sine-wave input or continuous wave (CW) as the LO input, the output IF component in the output current becomes gonvrf/4. This in turn changes the power ratio from –3.92 dB to –6 dB, due to lower LO input power. This decrease in LO power impacts the mixer’s ability to drive the conductance between off/on states, degrading output power and noise figure.

In general, most mixers have from 4.5 to 9 dB of conversion loss. This depends on mixer type and any additional losses including mixer imbalance, balun mismatch, and diode series resistance. Wider-bandwidth mixers are more susceptible to higher conversion loss as they struggle to maintain balance over the complete input bandwidth. The conversion gain affects the overall system automatic gain control (AGC) planning, DPD system algorithms, and sensitivity planning.

Noise
As a mixer performs frequency translation, it adds noise to the signal. The signal-to-noise ratio (SNR) at the input compared to SNR at the output under hot conditions is known as noise factor. This measurement is a capture of the noise while the device is turned on to capture the noise energy emitted under hot or conductance conditions. This figure is then compared to the noise power during cold or off conditions. Remember the calculation of cascaded networks and total noise using noise factor:

Noise factor F = (SNR)In/(SNR)Out (5)
Noise figure NF = 10log(F) (6)

From the cascade noise figure in Equation 7, where G is the gain of the various stages, the first stages have the greatest impact. So in a basic receive system, a switch, filter, and low-noise amplifier (LNA) prior to the mixer all add to the noise factor of the overall system. Carefully selecting these components and the mixer can minimize the total noise and improve sensitivity.

Remember that the LO drive level affects both conversion gain and noise. As the LO power degrades, then, so does noise. There is a slight difference in how noise is defined for a double sideband (DSB) mixer and a single sideband (SSB) mixer. DSB means both the desired IF and image are available at the output (for all mixers discussed up to this point). SSB means that the image is ideally attenuated as much as possible.

DSB noise includes noise and signal contributions from both RF and image frequencies. For SSB noise, the image signal is theoretically missing, though the image noise is included. An ideal SSB has a noise figure twice that of a comparable DSB mixer.

Isolation
Isolation in a mixer is specified between: RF to IF; LO to IF; IF to RF; and LO to RF. Isolation measurements calculate the amount of power that leaks from one port to another. For example, to measure isolation from LO to RF, simply apply a signal to the LO port and measure the power of this input LO signal at the RF port.

Isolation is critical since the input signals, especially the LO, can be high enough to cause system performance degradation. LO leakage can interfere with an incoming signal by interfering with the RF amplifier or by radiating RF energy at the antenna port. Leakage of the LO to the IF output can compress the remaining IF blocks in the receiver lineup, causing processing errors.

Leakage of the RF to IF and vice versa indicates how well the circuit is balanced, which relates back to conversion loss. The better balanced the mixer, the lower the conversion loss; thus, there is better conversion loss flatness. Ideally, isolation specifications are as high as possible and incorporated with shielding and good layout practice on the final form-factor board design.

1-dB Compression Point
In the receive system, the mixer most likely sees the highest power of the entire system. So, linearity specifications are highly important and can determine many of the system specifications for the overall receiver and transmit capability.

Under normal or linear operation, conversion loss in a mixer is constant, regardless of RF power. This means that as you increase the input power in 1-dB steps, the output power also increases by 1 dB. At the P1dB compression point, the input power increases such that the output does not increase linearly with input power. This is where the mixer conversion loss increases 1 dB from the ideal (Fig. 2).

Operating the mixer at or above the P1dB point distorts the wanted IF or RF signal as well as increases the spurious content in the spectrum. The 1-dB compression point of the complete chain impacts the system’s dynamic range. Typical P1dB specs for mixers range from 0 to 15 dB. The higher the P1dB, the better the performance and, in turn, potentially better system dynamic range.

Third-order intercept
Third-order intercept (IP3) impacts system performance similar to P1dB. Poor third-order intermodulation performance directly relates to IP3 and can raise the noise floor under real operating conditions. This can appear to reduce the sensitivity of the radio receiver, which in turn can degrade the performance of the overall radio communications system. Thus, the higher the IP3 point, the better.

For IP3 measurements we apply two input signals of the same power, F1 and F2, to the RF input (assuming this is a down-conversion process). For the IP3 calculation, we have third-order intermodulation distortion (IMD3) products of interest at (2F2 – F1) – FLO and (2F1 – F2) – FLO due to their close proximity to the IF output of concern, which we subtract from the IF frequency output for our calculation:

The IP3 point is a theoretical value derived from IMD3’s terms since the actual IP3 point cannot be reached. The mixer’s output stage saturates before IP3 can be achieved. Typically for passive mixers, IP3 is at least 15 dB above the P1dB point for higher-frequency signals and 10 dB above the compression point for lower-frequency signals.

Spurs
The process of mixing produces output products of the sum and difference of input signals as well as a vast number of additional unwanted spurious signals (Fig. 3). These include the fundamentals of the mixer’s inputs and outputs, their harmonics (nRF, mLO, or kIF), and intermodulation products, nRF ± mLO (down-conversion) and nLO ± mIF (up-conversion).

We define these intermodulation products as unwanted mixing products. These spurious responses are due to the harmonic mixing of the input signal and the LO. The levels of these spurious signals depend on a number of factors. The signal input levels, load impedance, temperature, and frequency all impact the spurious signals.

Harmonic products (nRF, mLO, kIF) increase exponentially to the power of the output signal. These unwanted products can be simply expressed mathematically in equations showing the increase in power:

Fundamental: VOut = Acos(ωt) (10)
Second harmonic is the square: A2cos(2ωt) (11)

Third harmonic is the cube:
A3cos(3ωt) (12)

Nonlinear distortion products significantly impact wideband systems due to the complexity of filtering and the wide range of frequency performance impacted by these spurious responses. Narrowband applications are impacted only by those in the pass band. With adequate band pass filtering, most undesired products can be effectively attenuated. However, as mentioned earlier, IMD3 products are close to the desired signal so it is very difficult to filter out such a signal.

Image (sideband suppression)
One signal affecting both the receive and transmit paths for a typical mixer is the image. A signal at the RF input port 2IF away from the incoming signal will be converted directly to the same IF as the desired input signal in down-conversion. Techniques such as filtering and using multiple IF frequency stages and image reject mixers (IRMs) can minimize the impact of this unwanted signal.

The image is simply the “other” output from the desired output signal per system planning because the output of any simple mixer includes the sum and difference by default of mixing. A more sophisticated mixer design that enables higher rejection of the image at the output of the mixer is called the SSB or in-phase/quadrature (I/Q) modulator. For example, the Texas Instruments TRF372017 is a highly integrated phase-locked loop/voltage-controlled oscillator (PLL/VCO) I/Q modulator.

DC offset
Another key component of the output spectrum is LO leakage, or dc offset and carrier suppression. Isolation impacts this functionality of mixers, and dc offset is a measurement of imbalance in the mixer. This specification is of particular importance in I/Q modulators and demodulators. As they are inherently two mixer devices, these mixers can have some imbalance affected by a difference in gain or biasing between the two internal mixers.

Specifically, for zero-IF systems using these modulators and demodulators, the dc offset (carrier suppression) impairs performance as the leakage will be within the signal bandwidth. The dc offset at the mixer output will be at the LO frequency and, depending on the dc offset, dominates error if the imbalance is high enough within the device (Equation 13). Consequently, if a 1-VRMS signal has a 10-mV dc offset:
CS = –40 dBc (14)

LO drive level
LO drive level is a specification for designers to consider closely in a mixer. The available output power of a system’s LO may limit mixer options within a design. Insufficient drive levels can degrade overall mixer performance. Too much drive level can degrade performance as well as damage the device. Active mixers tend to need less LO power than passive mixers and have more flexibility in the range of LO power for full mixer performance.

Mixer Topologies
Mixers can be passive or active. Passive mixers use diodes and passive components for mixing and filtering. Generally, passive mixers have better linearity but higher conversion loss or noise. Additionally, we have single-balanced and double-balanced mixers. Single-balanced mixers have limited isolation, while double-balanced mixers have far better isolation between ports and increased linearity.

Most people are familiar with the basic Schottky diode double-balanced mixer. This is one of the highest-performing mixers available that requires little more than some well matched, low-loss baluns at the input and four-bridge configured diodes. For improved isolation, the output is tapped off the input signal port (not LO) for improved isolation. The low ROn and high-frequency performance of Schottky diodes makes this mixer an ideal choice with one drawback: it needs high LO power.

We have a wide variety of options for active mixers such as bipolar junction transistor (BJT) and FET mixers and the Gilbert cell topology that creates a true multiplicative multiplier, improving isolation and even-order harmonics. The Gilbert cell topology is by far the most popular active mixer design.

While these mixers can offer very high performance, we still need filtering and several IF stages to remove the image from the wanted output. The image is always 2IF away from the wanted IF signal, so that at low IF the filtering is more constrained. Increasing complexity for tunable systems, the filter must track the LO to maintain performance. This system may need several stages and filtering to properly eliminate the image correctly with a higher IF.

With an IRM, we can achieve image rejection through phase cancellation instead of filtering or multiple IF stages. The design starts with a quadrature IF mixer. This mixer incorporates two double-balanced mixers, a 90° splitter and a zero degree splitter. To function as an IRM, we simply add a 90° hybrid following the IF ports to separate the image and real signal, enabling the image output to be either terminated or available for further processing (Fig. 4).

As discussed earlier, there may be a mismatch within the two mixers internal to this type of design because some of the down-converted images are present at the desired IF output port. Image rejection is the ratio of the desired IF to the image at the output of the same port. To improve an IRM’s performance, good rejection matching is a critical design parameter.

For up-conversion, we have an SSB mixer or I/Q modulator. In the SSB IRM, the image and real outputs now become the inputs in this topology and the RFIn becomes the RFOut. Figure 5 simplifies this configuration with the input frequency noted as BB (baseband) or IF signal in the transmit path. Equations 15-21 show how this SSB or I/Q modulator can reject or attenuate the image.

BB I = Asin(ωmt) (15)
BB Q = Acos(ωmt) (16)

With LO through the phase splitter assuming a CW input, we have:

LO in-phase = sin(ωct) (17)
LO quad-phase = cos(ωct) (18)

 

Thus, using basic trigonometry identities the following is combined in the power combiner at RFOut (Equations 19 and 20). From this we see that the USB or upper sideband (ωc + ωm) components cancel and only the least significant bit (LSB) is left. The output is:

RFOut = RFIn-phase + RFQuad-phase = Acos((ωc – ωm)t) (21)

Clearly, this is in an ideal SSM where there is not an imbalance in the circuit. In the real world, however, the BJTs, FETs, and diodes are never perfectly balanced. There will be gain and phase mismatch and isolation will never be infinite, so there will be LO leakage at the RFOut port. Baseband or IF signals will not be perfectly balanced, nor will the LO input be ideal.

The two specifications that matter the most in choosing an I/Q modulator are sideband suppression and carrier leakage. The dc offset or carrier suppression is an unwanted output LO component and is a result of isolating the LO-RF port and the dc imbalance of the BB or IF signal. Sideband suppression is measured in dBc. This is the image component and taken relative to the output signal. It is a result of mismatch in gain and phase balance of the mixers.

References
1. Download the datasheet for the TRF372017 at www.ti.com/trf372017-ca.
2. For more information about modulators and demodulators, visit www.ti.com/modulators or www.ti.com/demodulators.
3. Gray, P.R., Hurst, P.J., Lewis, S.H., Meyer, R.G., Analysis and Design of Analog Integrated Circuits (4th Edition), Wiley, ISBN 0471321680
4. Razavi, B., RF Microelectronics, Prentice Hall, ISBN 0138875715
5. Chang, K., Bahl, I., Nair, V., Thallon, R., Murarka, S., Chow, T., Allen, E., RF and Microwave Circuit Design for Wireless Applications, Wiley-Interscience, ISBN 0471197734