The mixer is an essential building block in the receivers, which is responsible for frequency up-conversion and down-conversion. It is also an important component associated with the linearity of the front-end receivers. The first stage of mixer must have high linearity to handle the large input signals from LNA without significant intermodulation. Nonlinearity causes many problems, such as cross modulation, desensitization, harmonic generation, and gain compression, but even-order nonlinearity can be easily reduced by differential architecture. However, odd-order nonlinearity is difficult to be reduced, especially the third-order intermodulation distortion (IMD3). IMD3 is the dominant part of the odd-order nonlinearity.
Mixer is a three ports circuit, which are the RF port, the LO port and the IF port. It is a multiplication of two signals which are the RF signal amplified from the low noise amplifier and the signal from the local oscillator (LO) to achieve the function of frequency transformation. This is depicted by equation (2.4). Then the RF signal is down-converted to the intermediate frequency (IF).
(
cos 1)(
cos 2)
cos(
1 2)
cos(
1)
2
AB
A ω t B ω t
= ⎡⎣ω ω
+t
+ω ω
− 2t
⎤⎦ (2.4) From the equation (2.4), the multiplication of two signals at the frequencies of ω1 and ω2 together produce signals at the sum (ω1+ω2) and difference (ω1-ω2) frequencies. The amplitudes are proportional to the RF and LO amplitudes. The multiplications in the time domain would result in convolutions in the frequency domain. Thus, the mixer can responsible for frequency translation. In equation (2.4), signals at the frequency of (ω1+ω2) can be easily filtered out because they are far away from desired frequency in the frequency domain. The signals at the frequency of (ω1-ω2) are our desired outputs. In circuit implementations, the multiplication can beachieved by passing the input signal
A
cosω t
from RF through a switch driven by another signalB
cosω t
from LO. If the LO amplitude is constant, any amplitude modulation in the RF signal is transferred to the IF signal.The most important parameters for determining the performance of a mixer are power conversion gain, and linearity. We will describe these parameters in the subsequent contents.
2.4.2 Performance Parameters 2.4.2.1 Conversion Gain
One of important parameters of mixer’s characteristics is conversion gain, which is defined as the ratio of the desired IF output to the value of the RF input as shown in equation (2.5). In general, the conversion gain of the mixer has two types: one is voltage conversion gain and the other is power conversion gain.
The desired output IF power Conversion Gain
The input RF power
= (2.5)
Assuming input a sinusoidal signal and the output would include signals at integer multiples of the frequencies of the input signal as equation (2.6). In equation (2.6), the terms with the input frequency are called the fundamental signal, and the higher order terms are called the harmonics. The harmonics would cause performance degradations.
The output function of mixers is a compressive function of input levels. When the input level grows sufficiently high, the output eventually saturates and the conversion gain begins decreasing. If α3 holds a negative value, this phenomenon will happen. At small values of input level A, the second term is negligible and the gain remains
constant. The gain starts decreasing when the input level gets large as shown in equation (2.7).
2 3
1 4
Gain=α +α A (2.7)
2.4.2.2 Linearity
The mixers are assumed to be linear and time-invariant. The linearity is a significant parameter in the mixer design. Here we will introduce two parameters of linearity: P1dB and IIP3.
The IF output is proportional to the RF input signal amplitude ideally. However, as the input signal becomes large, the output signal fails to exhibit this characteristic. We use the value departing the ideal linear curve 1 dB as the referenced point, 1 dB compression point, shown in Fig. 2.8. The dashed line in Fig. 2.8 shows our desired output characteristics. The solid line shows the real characteristic. The 1dB compression point characterizes the input level where the output level is 1dB less than our desired output level. A higher 1dB compression point stands for a better linearity performance.
The linearity of a mixer can also be evaluated by intermodulations. The two-tone third-order intercept is often used to characterize mixer linearity. Ideally, each of two different RF input signals will be translated without interacting with each other, and we can only gain the desired IF signal from the output port. However, practical mixers will always exhibit some intermodulation effects. This is because that two or more different frequencies of input signals will degrade the linear region of the system. The third intercept point (IP3) is measured with two tone test. Two tones are closely placed and injected as input simultaneously. If we consider the region where the input level is small, the output characteristic is approximately linear. The third-order
intercept is the intersection of these two curves as illustrated in Fig. 2.9 which is the extrapolation of the signal line and the third-order harmonic line. The higher intercept, the more linear.
1dB
A 1dB RF input power IF output
power
Fig. 2.8 P1dB
3rd intercept point
RF input power IF output
power
3rd intermodulation product IF power
Fig. 2.9 IIP3
2.4.2.3 Isolation
Another important parameter of mixer is isolation, which shows the interaction among RF, IF and LO ports. The isolation between each two ports of the mixer is important. The LO to RF feedthrough is means the LO leakage to the LNA and (or) leakage to the antenna. The RF to LO feedthrough allows strong interferers in the RF path to interact with the LO driving the mixer. The LO to IF feedthrough is also important. If substantial LO signal exists at the IF output, the following stage may be
desensitized. The feedthrough can be reduced largely by use double balanced mixers.
The RF to IF isolation means the signal in the RF path directly appears in the IF. In the homodyne receivers, this is a critical issue with respect to the IMD2 problem.
2.4.3 The Basic Mixer Architecture
The implementation of CMOS down-conversion mixer can be passive or active.
The simple passive mixer is shown in Fig. 2.10 It is usually using MOS transistor as a switch to modulate the RF signal by LO signal and down convert to IF band. Because passive mixer operates in the linear region, it has high linearity and excellent IIP3.
But it provides poor conversion gain and noise figure. The simple active mixer is presented in Fig. 2.11 The active mixer provides better conversion gain than passive mixer. Its conversion gain is decided by the product of the input conductance gm and load impedance to suppress the noise contributed by the subsequent stages. But the linearity of an active mixer is worse than that of a passive mixer.
RF
LO
IF
Fig. 2.10 Passive mixer
IF
RF
LO
Fig. 2.11 Active mixer
Chapter 3 The Design of 5.8GHz Bi-directional Amplifier
Based on the background, a bi-directional amplifier plays a significant role in the Retro-directional antenna system of active Van Atta arrangement. When a bi-directional is designed to possess the high gain, the circuit must be watched out for the isolation of signal in the input port so as to prevent the reflected signal from affecting the circuit performance of the input port. The contents of this chapter below will introduce the complete framework of this bi-directional amplifier using a 0.18 um CMOS process in detail and discuss the principles and considerations of each section.