Analysis of mixers and modulators in wireless communications

“In wireless communication systems, signals must be up-converted or down-converted before signal propagation and processing. This frequency conversion step, traditionally known as mixing, is an integral part of the receive and transmit signal chain.

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In wireless communication systems, signals must be up-converted or down-converted before signal propagation and processing. This frequency conversion step, traditionally known as mixing, is an integral part of the receive and transmit signal chain.

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

In all wireless designs, mixers and modulators support frequency conversion and enable communication. They determine the basic specifications of the entire signal chain. They have the highest power in the receive signal chain, upconvert the signal from the digital-to-analog converter (DAC) in the transmit path, and implement a digital predistortion (DPD) system that affects the performance of the entire communication system.

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

How Basic Mixers Work

The simplest mixer is a multiplier. A mixer is actually an output signal that multiplies an input signal to generate a new frequency. RF modulators and demodulators are essentially mixers. These devices take baseband input signals and output RF modulated signals (and vice versa).

Since the factors that affect the mixer also affect the modulator, this article mainly discusses it from the perspective of the mixer. Receivers typically use down-conversion to process high-frequency RF signals, while transmitters convert low-frequency baseband signals to high-speed RF. All parts of the mixer act 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 an intermediate frequency (IF). The output signal contains the sum and difference of the inputs (Figure 1). We can explain these mixing output components mathematically:

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

With trigonometric identities, we can get an output that includes the sum and difference:

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

Depending on the IF frequency and system-level planning, multiple down-conversion processes and filtering may be required to obtain the signal quality required for signal processing. (LO > RF is injected on the local oscillator, RF > LO is injected under the local oscillator.)

The mixer in the up-conversion process is generally used after generating the baseband signal. In this process, IF is the input and RF is the output. In addition, the outputs are the sum and difference of the input signals.

Additional filtering at the input and output is required to reduce unwanted products and achieve desirable performance similar to the receive signal chain.

Conversion gain

Conversion gain is the primary metric for mixers and can be used for functional verification in production. 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 in terms of insertion loss.

Generally speaking, the conversion loss of most mixers is between 4.5 and 9 dB. It depends on the mixer type and all the additional losses like mixer unbalance, balun mismatch and Diode series resistance. Wideband mixers are more prone to higher conversion losses because they need to be balanced across the entire input bandwidth. The conversion gain affects the overall system automatic gain control (AGC) planning, DPD system algorithm and sensitivity planning.

noise

Mixers add noise to the signal as they perform frequency conversions. The signal-to-noise ratio (SNR) of the input relative to the SNR of the output in the hot state is called the noise figure:

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

It can be seen from the cascade noise figure (G is the gain of each stage) that the first stage has the greatest impact. Therefore, in a basic receiving system, switches, filters, and low-noise amplifiers (LNAs) before mixers all increase the noise figure of the overall system. Careful selection of these components and mixers can minimize overall noise and improve sensitivity.

Remember that the LO drive level affects conversion gain and noise. As the LO power decreases, so does the noise. Double sideband (DSB) mixers and single sideband (SSB) mixers define noise slightly differently. For DSBs, the output provides the required IF and mirror (for all mixers discussed so far). For SSB, mirroring is minimized.

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

isolate

Isolation in the mixer is specified between the following ports: RF to IF; LO to IF; IF to RF and LO to RF. The isolation metric calculates the leakage power from one port to another. For example, to measure LO to RF isolation, simply apply a signal to the LO port and measure the power of this incoming LO signal at the RF port.

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

RF to IF leakage and IF to RF leakage represent circuit balance performance, which is related to conversion losses. The better the balance of the mixer, the lower the conversion loss; therefore, the better the flatness of the conversion performance. Ideally, the isolation specification is as high as possible, with shielding and good layout on the final form factor board design.

1dB compression point

In a receiving system, the mixer is most likely the highest power device in the entire system. Therefore, the linearity specification is very important, it can determine many system specifications of the whole receiver.

Under standard or linear operating conditions, the mixer’s conversion loss is constant, independent of RF power. This means that when you increase the input power in 1dB steps, the output power will also increase by 1dB. At the P1dB compression point, the input power increases, the output does not increase linearly with the input power, and its value is 1dB lower than the linear output.

Running the mixer at the P1dB point or higher distorts the desired IF or RF signal while increasing the amount of spurs in the spectrum. The 1dB compression point of the complete signal chain affects the dynamic range of the system. A typical P1dB specification for 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) also affects system performance. Poor third-order intermodulation performance is directly related to IP3 and increases the noise floor under real operating conditions. This appears to reduce the sensitivity of the wireless receiver and correspondingly reduce the performance of the overall 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 downconversion process). To calculate IP3, due to being very close to the relevant IP output, we generate the relevant third-order intermodulation distortion (IMD3) at (2F2 C F1) C FLO and (2F1 C F2) C FLO, due to failure to reach the actual IP3 point , so the IP3 point is the theoretical value obtained from IMD3. The output stage of the mixer saturates before reaching IP3. Generally speaking, 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 produces the output of the sum and difference of the input signals 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: Spectrogram of mixer output showing all the different products produced. The desired signals are sum or difference frequencies, but note that unwanted images and second and third order signals are the result of harmonics. Filtering helps reduce these unwanted signals.

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

Due to the complexity of filtering and the breadth of frequency performance affected by these spurious responses, nonlinear distortion products can have a considerable impact on wideband systems. Narrowband applications are only affected by the distortion products of the passband. Most of the harmful products can be effectively reduced with adequate bandpass filtering. However, as mentioned earlier, the IMD3 product is very close to the desired signal, making it difficult to filter out such signals.

Mirror (Sideband Suppression)

One type of signal that affects both the receive and transmit paths of a typical mixer is an image. Signals at a distance of 2IF from the input signal will be directly converted to the same IF as the desired input signal during downconversion. Methods such as filtering and the use of multiple IF stages and image reject mixers (IRMs) can minimize the effects of this unwanted signal.

Mirroring is the “other” output from the desired output signal according to the system plan, since the output of any simple mixer contains the sum and difference of the mixing frequencies. Advanced mixer designs that can achieve higher image rejection at the mixer output are called SSBs 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 critical 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 especially 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 zero-IF systems using these modulators and demodulators, the DC offset (carrier suppression) degrades performance due to leakage within the signal bandwidth.

LO drive level

The LO drive level is a specification in a mixer that requires careful consideration by the design engineer. The available output power of the system LO may limit the mixer selection scheme in the design. Insufficient or too high drive levels can degrade overall mixer performance. At the same time, driving the level too high may also damage the device. Active mixers tend to require less LO power than passive mixers, and offer greater flexibility in the LO power range to achieve full 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 losses or noise. There are also single-balanced mixers and double-balanced mixers. Single-balanced mixers have limited isolation, while double-balanced mixers have much better port-to-port isolation and are more linear.

Most people are familiar with the basic Schottky diode double-balanced mixer. This mixer is one of the highest performing mixers, requiring only a few well-matched, low-loss baluns at the input and diodes in a four-bridge configuration. For higher isolation, the output signal is split out at the input signal port (not LO). The low on-resistance (Ron) and high frequency performance of Schottky diodes make this mixer ideal, but it has one drawback: the need for high LO power.

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

While these mixers can provide extremely high performance, we still need filtering and multiple IF stages to remove the image from the desired output. The mirror is always 2IF away from the desired IF signal. Due to the increasing complexity of tunable systems, the filter must track the LO to maintain performance. Such a system may require multiple stages and filtering in order to completely eliminate higher IF images.

With IRM, we can achieve ambient image suppression through phase cancellation without filtering or multiple IF stages. The design begins with a quadrature IF mixer. This mixer incorporates two double-balanced mixers, a 90° shunt and a zero-degree shunt. To implement the functionality of the IRM, it is only necessary to add a 90° hybrid circuit after 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 reject mixers are the most popular among receivers. It removes sum or difference frequency products by phase shifting and produces a single output without filtering. The LO is phase-shifted by 90°, producing in-phase and quadrature-phase signals, which are mixed with the incoming RF signal. The mixer outputs are then phase shifted by 90° from each other, thereby removing some of the products.

Based on the discussion above, the two mixers inside this design may not be matched, so there is some downconversion image 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 the performance of IRM, good suppression matching is a key design parameter.

Figure 5: A single-sideband upconverter or modulator is used in the transmit signal chain. This process is similar to the image-reject mixer of the receive signal chain (Figure 4). The baseband (BB) signal is applied to in-phase (I) and 90° phase shifted (Q) mixers and mixed with the LO signal split into 90° phase shifted components. Added mixer output, single product or sideband as RF output.

As for upconversion, we have SSB mixers or I/Q modulators. In SSB IRM, the mirror and valid outputs are now inputs in this topology, and RFIn is RFOut. Figure 5 simplifies this configuration with the BB (baseband) input frequency or IF signal in the transmit path. The following equations show how such an SSB or I/Q modulator suppresses or reduces images.

BB I = Asin(ωmt)
BB Q = Acos(ωmt)

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

LO in-phase = sin(ωct)
LO quadrature = cos(ωct)

Therefore, by trigonometric identities, the following parts are integrated into the power combiner of RFOut. From here we can see that the upper sideband (ωc + ωm) device (USB) is removed and only the least significant bit (LSB) is preserved. The output is:

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

Obviously, this is an ideal SSM with no imbalance in its circuit. However, in the real world, BJTs, FETs and diodes are never ideally balanced. There will always be a gain and phase mismatch and the isolation will be limited, so there will be LO leakage at the RFOut port. Baseband or IF signals will not be ideally balanced, nor will the LO input.

The two most influential metrics when choosing an I/Q modulator are sideband suppression and carrier leakage. DC offset or carrier suppression is a detrimental output LO component that is a result of the DC imbalance between the isolated LO-RF port and the BB or IF signal. Sideband rejection is measured in dBc and is the result of a mismatch in mixer gain and phase balance.