# Analysis of mixers and modulators in the field of high-speed communications

In high-speed wireless communication systems, signals must be up-converted or down-converted before they can be propagated and processed. This frequency conversion step is traditionally called mixing, and it is an indispensable process in the receiving and transmitting signal chain.

As a result, mixers and modulators have become the basic building blocks of radio frequency (RF) systems. As wireless communication standards continue to evolve, it is important to look at the characteristics of these components and understand how mixers affect overall system performance.

In all wireless designs, mixers and modulators support frequency conversion and realize communication. They determine the basic specifications of the entire signal chain. Their receive signal chain has the highest power, up-converts the signal from the digital-to-analog converter (DAC) in the transmission path, and implements a digital predistortion (DPD) system, which affects the performance of the entire communication system.

So, how does the basic mixer work? What are the important specifications to consider? What mixer and modulator schemes are currently available to improve and simplify system design?

Basic mixer working principle

The simplest mixer is a multiplier. Audio mixers only increase the signal, and RF mixers actually increase the input signal to generate an output signal at a new frequency. RF modulators and demodulators are essentially mixers. These devices take baseband input signals and output RF modulated signals (and vice versa).

Because the factors that affect the mixer will also affect the modulator, this article mainly discusses it from the perspective of the mixer. Receivers generally use down-conversion to process high-frequency RF signals, while transmitters convert low-frequency baseband signals into high-speed radio frequencies. All parts of the mixer are like loads and sources.

In the first example, we take the following frequency conversion as an example. The two inputs are RF and local oscillator (LO). The output is intermediate frequency (IF). The output signal contains the sum and difference of the input (Figure 1). We can mathematically explain these mixing output components through Equations 1-3:

RF input = A1sin (ω1t + φ1) (1)

LO input = A2sin (ω2t + φ2) (2)

Output IF = A1A2sin (ω1t + φ1) sin (ω2t + φ2) (3)

Through the trigonometric identities, we can get the output including sum and difference:

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

To obtain the signal quality required for signal processing, multiple down-conversion processes and filtering may be required, depending on the IF frequency and system-level planning. (LO “RF up injection type for local oscillator, RF “LO down injection type for local oscillator.)

The mixer in the up-conversion process is generally used in the early stage after the baseband signal is generated. In this process, IF is input and RF is output. In addition, the output is the sum and difference of the input signal.

Additional filtering is required at the input and output to reduce harmful products and achieve ideal performance similar to the received signal chain.

Conversion gain

The conversion gain is the main measure of the mixer and can be used for functional verification in production. The conversion gain is the ratio of the output signal level to the input signal level, usually expressed in dB. The conversion loss of a passive mixer is generally expressed by the insertion loss.

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

If the LO input is a continuous sine wave input or continuous wave (CW), the output IF component in the output current is gonvrf/4. Since the LO input power is low, the power ratio changes from –3.92 dB to –6 dB accordingly. The decrease in LO power will affect the conduction drive capability between the on/off states of the mixer, thereby reducing the output power and noise figure.

Generally speaking, the conversion loss of most mixers is between 4.5 and 9 dB. This depends on the mixer type and all additional losses such as mixer unbalance, balun mismatch and diode series resistance. Broadband mixers are more prone to higher conversion loss because they need to maintain a balance across the entire input bandwidth. The frequency conversion gain will affect the overall system automatic gain control (AGC) planning, DPD system algorithm and sensitivity planning.

noise

The mixer will bring noise to the signal when it performs frequency conversion. The input signal-to-noise ratio (SNR) relative to the output SNR in the heating state is called the noise figure. This metric is the noise captured when the device is turned on to capture the noise energy emitted in the heating or conducting state. This value is then relative to the noise power in the cooling or off state. Remember to use the noise figure to calculate the cascaded network and the total noise formula:

Noise figure F = (SNR) In/(SNR) Out (5)

Noise figure NF = 10log (F) (6)

It can be seen from the cascaded noise figure in Equation 7 (G is the gain of each stage) that the first stage has the greatest impact. Therefore, in the basic receiving system, the switch, filter, and low noise amplifier (LNA) before the mixer all increase the noise figure of the overall system. Careful selection of these components and mixers can minimize total noise and increase sensitivity.

Keep in mind that the LO drive level affects the conversion gain and noise. As the LO power drops, so does the noise. Double sideband (DSB) mixers and single sideband (SSB) mixers have slightly different definitions of noise. For DSB, the output provides the required IF and image (for all the mixers discussed so far). For SSB, mirroring will be reduced as much as possible.

DSB noise includes noise and signals from RF and image signal frequencies. For SSB noise, the image signal is theoretically lost (although the image noise is included). The noise figure of an ideal SSB mixer is twice that of similar DSB mixers.

isolate

Isolation in the mixer is specified between the following ports: RF and IF; LO and IF; IF and RF and LO and RF. The isolation measurement calculates the leakage power from one port to another. For example, to measure the isolation from LO to RF, you only need to apply a signal to the LO port, and then measure the power of the input LO signal at the RF port.

Since the input signal (especially LO) is high enough to cause system performance degradation, isolation is critical. LO leakage can interfere with the input signal by interfering with the RF amplifier or radiating RF energy at the antenna port. Leakage from the LO to IF output can compress the remaining IF units in the receiver array, causing processing errors.

The leakage from RF to IF and the leakage from IF to RF represent circuit balance performance, which is related to conversion loss. The better the balance performance of the mixer, the lower the conversion loss; therefore, it also has a better flatness of the frequency conversion performance. Ideally, the isolation specification should be as high as possible, and the final profile board design should have shielding and a good layout.

1dB compression point

In the receiving system, the mixer is most likely the most powerful device in the entire system. Therefore, the linear specification is very important. It can determine the many system specifications and transmission capabilities of the entire receiver.

Under standard or linear operating conditions, the conversion loss of the mixer is constant and has nothing to do with the RF power. This means that when you increase the input power by 1dB, the output power will also increase by 1dB. At the P1dB compression point, the input power is increased so that the output does not increase linearly with the input power. This is also the reason why the conversion loss of the mixer is 1dB higher than the ideal value (Figure 2).

Running the mixer at the P1dB point or higher will distort the required IF or RF signal and increase the amount of spurs in the spectrum. The 1dB compression point of the complete signal chain will affect the dynamic range of the system. The typical P1dB specification of a mixer is between 0 and 15 dB. The higher the P1dB, the higher the performance and the correspondingly better the system dynamic range.

Third-order intercept point

Similar to P1dB, the third-order intercept point (IP3) will also affect system performance. Poor third-order intermodulation performance is directly related to IP3 and will increase the noise floor under real operating conditions. This seems to reduce the sensitivity of the wireless receiver and correspondingly reduce the performance of the entire wireless communication system. Therefore, the higher the IP3 point, the better.

To measure IP3, we apply two input signals F1 and F2 of the same power to the RF input (assuming this is a down-conversion process). To calculate IP3, since it is very close to the relevant IP output, we generate the relevant third-order intermodulation distortion (IMD3) in (2F2 – F1) – FLO and (2F1 – F2) – FLO. We remove this distortion from the intermediate frequency output, The following calculation results are obtained:

Since the actual IP3 point is not reached, the IP3 point is the theoretical value obtained from IMD3. The output stage of the mixer saturates before reaching IP3. Generally for passive mixers, the IP3 of high-frequency signals is at least 15 dB above P1dB, and the IP3 of low-frequency signals is at least 10dB above the compression point.

Spurious signal

The mixing process will produce the output product of the sum and difference of the input signal and a large number of additional unwanted spurious signals (Figure 3). These spurious signals include the basic mixer input and output, its harmonic products (nRF, mLO or kIF) and intermodulation products, nRF ± mLO (down conversion) and nLO ± mIF (up conversion).

Figure 3: The spectrogram of the mixer output shows all the different products produced. The required signal is the sum frequency or difference frequency, but please note that the harmful image signal and the second and third order signals are the result of harmonics. Filtering helps reduce these harmful signals.

We define these intermodulation products as harmful mixing products. These spurious responses are caused by the harmonic mixing of the input signal and the LO. The level of these spurious signals depends on many factors. The signal input level, load impedance, temperature and frequency all affect spurious signals.

Harmonic products (nRF, mLO or kIF) increase the power of the output signal exponentially. These harmful products can be simply mathematically expressed in accordance with the following equation showing power increase:

Basic: VOut = Acos (ωt) (10)

The second harmonic is the second power: A2cos(2ωt) (11)

The third harmonic is the third power:

A3cos (3ωt) (12)

Due to the complexity of filtering and the wide range of frequency performance affected by these spurious responses, nonlinear distortion products can have a considerable impact on broadband systems. Narrowband applications are only affected by the distortion products of the passband. Adequate band-pass filtering can effectively reduce most harmful products. However, as mentioned earlier, the IMD3 product is very close to the desired signal, so it is difficult to filter out such a signal.

Mirror (sideband suppression)

A signal that affects both the receiving path and the transmitting path of a typical mixer is an image. The signal from the RF input port 2IF of the input signal will be directly converted into the same IF as the required input signal during the down-conversion process. Methods such as filtering and the use of multiple IF stages and image rejection mixers (IRM) can minimize the impact of this unwanted signal.

Mirroring is the “other” output from the required output signal according to the system plan. This is because the output of any simple mixer contains the sum and difference of mixing. Advanced mixer designs that can achieve higher image rejection at the mixer output are called SSB or in-phase/quadrature (I/Q) modulators. For example, TI’s TRF372017 is a highly integrated phase-locked loop/voltage-controlled oscillator (PLL/VCO) I/Q modulator.

DC bias

Another key part of the output spectrum is LO leakage or DC offset and carrier suppression. Isolation affects this function of the mixer, and the DC offset is a measure of the unbalance of the mixer. This specification is particularly important in I/Q modulators and demodulators. Since the I/Q modulator and demodulator are themselves two mixers, the partial imbalance of these mixers is affected by the gain or offset difference between the two internal mixers.

Specifically, for a zero-IF system using these modulators and demodulators, because of leakage in the signal bandwidth, DC offset (carrier suppression) will degrade performance. The DC offset at the output of the mixer will be at the LO frequency. Depending on the DC offset, if the imbalance within the device is high enough, the DC offset will affect the error (Eq. 13). Therefore, if the 1VRMS signal has a DC offset of 10mV, then:

CS = –40 dBc (14)

LO drive level

The LO drive level is a specification that needs to be carefully considered by the design engineer in the mixer. The available output power of the system LO may limit the mixer options in the design. Insufficient drive level will reduce the overall mixer performance. Too high drive level will degrade performance and damage the device at the same time. Compared with passive mixers, active mixers often require less LO power, and the LO power range has higher flexibility to obtain complete mixer performance.

Mixer topology

Mixers are divided into passive mixers and active mixers. Passive mixers use diodes and passive components for mixing and filtering. Passive mixers generally have higher linearity, but higher conversion loss or noise. In addition, there are single balanced mixers and double balanced mixers. Single balanced mixers have limited isolation, while double balanced mixers have much better isolation between ports and higher linearity.

Most people are familiar with the basic Schottky diode double-balanced mixer. This mixer is one of the highest performance mixers, and only needs some well-matched, low-loss baluns and diodes with a four-bridge configuration at the input. In order to obtain higher isolation, the output signal is split at the input signal port (non-LO). The low Ron and high frequency performance of Schottky diodes make this mixer an ideal choice, but it has one disadvantage: it requires high LO power.

We have a variety of active mixer options, including bipolar junction transistor (BJT) and FET mixers, and Gilbert cell topologies that create true multipliers to improve isolation and even harmonics. The Gilbert cell topology is by far the most popular active mixer design.

Although these mixers can provide extremely high performance, we still need filtering and multiple IF stages to remove the image from the desired output. The image is always 2IF away from the required IF signal, so that the filtering at the low IF end is more suppressed. Due to the increasing complexity of tunable systems, the filter must track the LO to maintain performance. Such systems may require multiple stages and filtering in order to completely eliminate the higher IF images.

When using IRM, we can achieve ambient image suppression through phase cancellation instead of filtering or multiple IF stages. The design starts with the quadrature IF mixer. This mixer integrates two double-balanced mixers, a 90° splitter and a zero-degree splitter. To realize the function of IRM, it is only necessary to add a 90° hybrid circuit behind the IF port to separate the mirrored and real signals, so that the mirrored output is terminated or used for further processing (Figure 4).

Figure 4: Image rejection mixers are the most popular in receivers. It can remove the sum or difference frequency products by phase shifting to produce a single output without filtering. The LO performs a 90° phase shift, produces in-phase and quadrature phase signals, and mixes with the input RF signal. Then the mixer outputs are phase-shifted by 90° with each other to remove some of the products.

Based on the discussion above, the two mixers inside this design may not match because some down-conversion mirroring appears at the required IF output port. Mirror rejection is the ratio of the required IF to the mirror image of the output of the same port. In order to improve the performance of IRM, good suppression matching is a key design parameter.

Figure 5: Single-sideband upconverters or modulators are used in the transmit signal chain. This process is similar to the image rejection mixer of the receive signal chain (Figure 4). The baseband (BB) signal is applied to the in-phase (I) and 90° phase shift (Q) mixers, and mixed with the LO signal divided into 90° phase shift components. The mixer output is added, and a single product or sideband is the RF output.

As for upconversion, we have SSB mixers or I/Q modulators. In SSB IRM, the mirror and valid output are now the inputs in this topology, and RFIn is RFOut. Figure 5 simplifies this configuration by BB (baseband) input frequency or IF signal in the transmit path. Equations 15-21 show how this SSB or I/Q modulator can suppress or reduce the image.

BB I = Asin (ωmt) (15)

BB Q = Acos (ωmt) (16)

When LO applies a CW input through a phase split circuit:

LO in phase = sin (ωct) (17)

LO orthogonal = cos(ωct) (18)

Therefore, through the triangular identities, the following parts are integrated into the RFOut power combiner (Equations 19 and 20). From here we can see that the upper sideband (ωc + ωm) device (USB) is removed, and only the least significant bit (LSB) is retained. The output is:

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

Obviously, this is an ideal SSM, and there is no imbalance in its circuit. However, in the real world, BJTs, FETs, and diodes have never achieved an ideal balance. There will always be a gain and phase mismatch, and isolation will be limited, so there will be LO leakage at the RFOut port. The baseband or IF signal will not achieve the ideal balance, and the LO input will not be ideal.

The two most influential specifications when choosing an I/Q modulator are sideband suppression and carrier leakage. DC offset or carrier suppression is the harmful output LO component, which is the result of the DC imbalance between the LO-RF port and the BB or IF signal. Sideband suppression is measured in dBc. This is the image component, which is a specification relative to the output signal. It is the result of a mismatch in mixer gain and phase balance.