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The LNA is the first block in most receiver front ends whose main function is to provide enough gain to overcome the noise of subsequent stages (such as a mixer). Aside from providing this gain while adding as little noise as possible, an LNA should accommodate large signals without distortion, and frequently must also present specific impedance, such as 50 ohm to the input source.
The overall noise factor of the receiver front end is dominated by the first few stages and can be approximated by the formula:
The noise of the subsequent stages is reduced by the gain of the LNA, and the noise of the LNA, is injected directly into the received signal. Thus the LNA needs high gain and low noise.
The topology of an LNA can be broken down into three into three stages: an input matching network, the core amplifier and an output matching network. The input/output matching networks are passive consisting of inductors, capacitors, and resistors. The objective of the input matching network is to ensure optimum noise performance as well as stability at the input. It also provides proper power matching between the antenna and the LNA. The output matching network ensures stability at the output.
Before analyzing different CMOS LNA architecture we must first be aware of the performance metrics for the LNA and their acceptable values.
As mentioned above, since the LNA is the first stage in the receive path, its noise figure directly adds to that of the system. For a typical LNA in the heterodyne system, the NF should not exceed 2db.
The minimum gain of an LNA in a heterodyne architecture is governed by three parameters: the loss of the image reject filter, noise figure and of the mixer. A gain of 20dB in the LNA adequately suppresses the input referred noise while maintaining a reasonable equivalent.
The LNA in heterodyne architecture is designed to have input impedance of 50. This is because the bandpass filter following the antenna is usually designed to be in various transceiver systems and must therefore operate with a standard termination impedance of 50. If the source and load impedances seen by the filter deviate significantly from 50 then the passband and stopband characteristics of the filter exhibits considerable loss and ripples.
In heterodyne architecture, the LNA output impedance must also be equal to 50so as to drive the image reject filter with minimum loss and ripple.
The reverse isolation of the LNA determines the amount of LO signal that leaks from the mixer to the antenna. This leakage arises from capacitive paths, substrate coupling and bond wire coupling.
The next issue while designing the LNA is stability. The LNA should be unconditionally stable which means that with any load present to the output or output of the device, the circuit will not become unstable - will not oscillate. Instabilities are primarily caused by three phenomena: internal feedback of the transistor, external feedback around the transistor caused by external circuit, or excess gain at frequencies outside of the band of operation.
The first design technique that we consider is using a common source amplifier [figure.2 (a)] to design a LNA. By virtue of its transconductance, the MOSFET converts variations in its gate source voltage to a small signal drain current which can pass through a resistor to generate an output voltage. In the amplifier, represents the parasitic capacitance of and the input capacitance of the next stage. Since the transconductance of MOSFETS is low, the voltage gain of this circuit is low making the noise contributed by significantly high. To increase voltage gain, is replaced by a current source. As the bias current and drain voltage of strongly depend on the supply voltage, a dc feedback network can be used to define the operating point. This results in the circuit shown in figure.2 (b). The key idea here is that the bias current is reused to provide a higher equivalent transconductance + and thus higher gain.
Fabricated in a 0.5- CMOS technology and operating from a 2.7-V supply, the 900-MHz LNA of figure.2 (b) exhibits a minimum noise figure if 1.9dB, a gain of 15.6 dB, and power dissipation of 20mW.
Figure 2 (a) Common-source stage with resistive load (b) LNA
However, due to the inherently high noise figure of the common source stage, in most CMOS applications where the noise figure is critical issue, a cascode LNA with inductive degeneration is preferable.
The purpose of a mixer is to translate a high frequency input signal to a lower frequency output signal, by "mixing" (multiplying) it with a reference signal provided by a local oscillator, since filtering, and circuit design become much easier at lower frequencies. Thus at the core of all mixers presently in use is a multiplication of two signals at different frequencies in the time domain, resulting in a third signal at the desired frequency. The use of multiplication can be easily seen from the following trigonometric equation:
The output thus, presents signals at the sum and difference frequencies of the input signals with amplitudes equal to the product of the input signal amplitudes. Hence if one of the amplitudes is constant, any modulation of the other will be transferred to the output. In conclusion, if one of the signals is a Radio Frequency (RF) signal at high frequency and varying amplitude, the other is a Local Oscillator (LO) signal, at a known frequency and amplitude, the multiplication will produce the sum, which can be filtered out if not needed, and difference, which will be the desired output, signals of the inputs with the amplitude modulation of the RF signal. Depending on the chosen receiver architecture, the output signal can be located at an Intermediate Frequency (IF), or in the baseband, but for the remainder of this section we will consider the first case, so the inputs of the mixers presented will be denoted RF and LO, while the output as IF.
Another important statement about mixers is that they are nonlinear devices, since nonlinearity is fundamentally necessary to generate new frequencies.
Before we present and compare the different mixer designs, we will enumerate and define the most significant characteristics of mixers.
Conversion Gain(or loss) is defined as the ratio of the desired IF output to the value of the RF input. Unlike LNAs mixers don't necessarily have high gain, since amplifying the input signal is not their primary function, and noise figures must also be considered when designing them. Nevertheless having a conversion gain is excess of unity is often convenient and desirable.
Noise figure in case of a mixer is defined as the signal-to-noise ratio at the RF port divided by the signal-to-noise ratio at the IF port. Since the IF is simply the magnitude of the difference between the RF and LO frequencies, signals above and below LO by will produce IF outputs at the same frequencies. Thus it can be stated that at the input of every mixer there are actually two frequencies that will generate the desired intermediate frequency. One is the desired RF signal and the other is called the image signal. In the usual case, where only the RF signal contains useful information the noise figure measured is called single-sideband noise figure (SSB NF), in the rare case when both RF and image signals contain useful information the noise figure measured is called double sideband noise figure(DSB NF). Mixers are much noisier devices than LNAs mainly because noise form frequencies other than the desired RF can be mixed down to the IF.
Linearity in mixers is usually characterized with the 1-DB compression point, or with the two-tone third-order intercept. Ideally we would like the IF output to be proportional to the RF input signal amplitude, but real mixers, much like other devices have a limit, beyond which the output has sub-linear dependence on the input. This point is usually the 1-DB compression point in the case of a mixer. The two-tone third-order intercept is also a relevant way to evaluate mixer linearity because it simulates the real-world scenario in which both a desired signal and a potential interferer feed the mixer input. In the ideal case these two should translate without interacting with each other, but practical mixers always exhibit some intermodulation effects and these can be measured with the third order intercept point.
Isolation is a parameter of great practical importance. It represents the level of interaction between the mixer inputs and output. Minimizing interaction between RF LO and IF ports is highly important to assure the correct functionality of the mixer. For instance, since the LO power is generally large compared to the RF signal, any LO feed-through can cause problems is subsequent stages in the signal processing chain. Isolating LO from RF is also important because strong LO signals can propagate all the way back to the antenna, where they can radiate and cause interference to other receivers.
Spurs are undesired signals that emerge ultimately from the output of the mixer as the result of mixing down a variety of unwanted frequency components, like harmonics of some signals. Evaluation of mixer spurs is straightforward in theory, but highly tedious in practice.
After the definition of the most important characteristics of mixers, we can now proceed to the presentation of different mixer designs, and compare their performance based on these parameters. We will categorize all presented mixers in the Active Mixers and Passive Mixers category. The main difference between an active and a passive mixers is that while the first provides a positive gain at the cost of dissipating quiescent power, and having a higher distortion performance, the second produces a negative gain(loss), requires only dynamic power and has excellent distortion performance. Another difference between the two categories is that most of the active mixers operate in the continuous time domain, while some passive mixer structures operate in the continuous time domain and others in the sampled data domain. Passive mixers operating in the sampled data domain are called sampling mixers, while those operating in the continuous time domain are referred to as switching mixers. The final difference is that while active mixers convert the input RF voltage to current and perform the multiplication of the input signals in the current domain, passive mixers, specifically switching mixers use the voltage domain to do the operation. We will concentrate our mixer presentation on active mixer designs but we'll also take a quick look at a passive switching mixer as well as a sampling mixer architecture.
The single balanced mixer is built from three CMOS transistors and represents the simplest form of an active mixer. Transistor M1 is used to convert the input RF voltage into current, while transistors M2 and M3 are alternately turned fully on and off by the input LO voltage steering all of the tail current from one side to the other of the IF output at LO frequency. This is equivalent to multiplying the current produced by M1 with a square wave which generates an output signal, that consists of sum and difference components, as a result of mixing the odd harmonics of the LO with the RF signal, as well as odd harmonics of the LO, as a consequence of the DC bias current multiplying with the LO signal. Because of these LOW signal components appearing directly at the output, this mixer is called single balanced. The performance analysis of this mixer reveals two major design issues, linearity and isolation. The main source of nonlinearity is the trans-conductance of the M1 transistor, since it cannot provide a perfect V-I conversion. Linearity can be enhanced through a process called source degeneration, by using either a resistance or an inductor. The second option (illustrated on the figure) is more desirable, particularly for low-voltage-low-power applications, because inductance has neither thermal noise to degrade noise figure, nor DC voltage drop to consume supply headroom. Single balanced mixers provide acceptable RF to IF port isolation by taking the IF output from both sides of the differential pair and cancelling out the RF feed-through, but as already mentioned, the LO to IF isolation is very poor because of the LO feed-through. The best way to improve this is to combine two single balanced mixers together to form what is known as a double-balanced or Gilbert mixer.
The double balanced (Gilbert) mixer is the most commonly used mixer. It consists of six CMOS transistor forming three source-coupled pairs (SCP). The bottom SCP is used for the V-I conversion which results is two currents, 180 degrees out of phase, at the tail of the upper SCPs also called the switching quad. These currents are alternately switched at LO frequency to the IF output by the upper two SCPs. These switches operate in opposite polarity as the result of how the LO signal is applied to their gates. First the two outer transistors turn fully on while the inner transistors are off, so the two generated currents can directly pass to the outputs. After the LO signal changes the outer transistors turn off and the inner transistors turn fully on so the generated currents can "cross" pass to the output. This behavior helps the mixer filter out by cancellation the unwanted LO and RF feed-through as well as other undesired signals. Thus double balanced mixers provide high port to port isolation and good spur rejection but they also have a very low noise figure and provide a high gain. Both noise sensitivity and gain can be improved by choosing the LO signal amplitude to be fairly large. Since the output amplitude of the mixer is formed by the product of the LO and RF signal amplitudes, the higher the LO amplitude, the bigger the conversion gain. However for a large enough LO the upper quad switches and no further increases occur. The noise figure also depends on the magnitude of the LO amplitude. With large amplitudes noise is minimized because the switching of the upper quad. When the transistors are off they don't degrade the noise figure, and when fully on, they behave as a cascade transistor which does not contribute significantly to noise. Usually -10 to 0 dB (100 to 300 mV) is a reasonable compromise between noise figure, gain and required LO power. If LO is too large, lot of current has to be moved into and out of the bases of the transistors during transitions which can lead to spikes in the signals and can actually reduce the switching speed and increase the LO feed-through. Another problem is caused by the parasitic capacitances between the sources of the upper SCPs, because these always need to be charged and discharged when the transistors are switched. If these capacitances are too large, the transistors take more time to switch and they switch for a smaller portion of the cycle. This can lead to waveform distortion as well as higher power consumption. Thus, too large LO signals can be just as bad as too small LO signal. Just as in the case of the single balanced mixer, linearity presents the biggest problem in designing these circuits. Mixers are inherently nonlinear devices, but they also have some linearity requirements, mainly because of the V-I translation of the input RF signal. This conversion needs to be linear because the RF input can contain channels at different frequencies and different amplitudes, and if the RF input circuitry were nonlinear, adjacent channels could inter-modulate and interfere with the desired channel. Source degeneration is the most effective method to improve linearity, but techniques called pre-distortion, feedback, feed-forward and piecewise approximation can also be used to further extend linearity.
Bulk driven mixer is another example for CMOS based active mixers. It has a very compact and power efficient design. At the core of this mixer are only four NMOS transistors which realize the switching action needed for the frequency translation as well as RF and LO feed-through filtering. As can be seen from the figure, the RF signal is applied to the bulk of the transistors to obtain the necessary trans-conductance and similarly to the Gilbert mixer the LO+ and LO- anti-phase signals applied to the gate switch the transistors alternately on and off. In the first phase, LO+ is larger than the threshold voltages of M1 and M4 so they are switched on allowing the RF input to directly pass to the IF output via the back gate trans-conductance. At the same time LO- is smaller than the threshold voltages of M2 and M3 so they are turned off. In the second phase, LO- turns the M2 and M3 transistors on while LO+ turns M1 and M4 off causing the output to change polarity. Thus the RF input is commutated by the action of the local oscillator on the gates of M1-4, and hence converted to the desired IF frequency. To obtain a reasonable gain the transistors when switched on are held in the saturation region by a sufficiently large VDS. The technology used in this mixer is also known as twin-well technology. Due to the exploitation of both the gate and the body trans-conductance, the bulk driven mixer core requires a low supply voltage and consumes less power. The circuit can work with a supply voltage as low as 1V and consumes 1.6mW however, this reduction in power consumption is not achieved at the expense of linearity of the mixer.
Active mixers first convert the incoming RF voltage into a current through a trans-conductor, whose linearity and noise figure limit the overall mixer linearity and noise figure. They also need a considerable amount of power in order to provide the best performance. Passive mixers try to switch the RF signal directly in the voltage domain to avoid the issues due to V-I conversion. Also they are attractive because their potential for extremely low-power operations. Considering that CMOS technology offers excellent switches, passive switching mixers are naturally realized in CMOS form.
The double balanced switching mixer is the passive counterpart of the Gilbert mixer. It consists of four CMOS transistors in a bridge configuration, driven by the LO signal in a way that at a given time only one diagonal pair is conducting, so the output is equal to and respectively. Thus the input is multiplied by a unit-amplitude square wave with an LO frequency so the output contains a lot of unwanted components but these can be filtered out at the next stage. As stated previously the conversion gain of this mixer is smaller than one and it has improved linearity since there is no V-I conversion phase so the source of any nonlinearity are the switching transistors. Because the LO power can be chosen much smaller than in the case of active mixers and there are less transistors required for the design this type of mixer needs less power and provides lower quiescent power dissipation.
The subsampling mixer is based on the observation that the information bandwidth of modulation is necessarily lower than the carrier frequency. Hence a high frequency signal sampled with lower frequency can produce data from which the down-converted low frequency output can be reconstructed, as shown in the figure. The theoretical advantage of this approach is that it may be easier to realize samplers that operate at a frequency well below that of the incoming RF signal. Hence a properly designed track-and-hold circuit like the one in the figure can serve as a subsampling mixer. The main issues of these circuits come from time-resolution problems, aperture jitter, and foremost a considerable noise boost at the output, since sampling operation not only converts the input signal but any noise present at the input stage as well. Subsampling mixers are particularly useful for applications, where the circuits that they feed into consist of sampled data circuits like A/D converters and IF amplifiers implemented in the sampled data domain.