Retro-directional antenna arrays are applied in many wireless communication systems, such as RF identification apparatuses and intelligent transport systems [1]-[4]. These kinds of antenna systems can reflect the received signals along the incident direction without any portended signals as shown in Fig. 2.1.
There are two familiar categories of retro-directional antennas. One is the type of phase-conjugated-array elements; the other is the form of Van Atta arrangement [5].
The former antenna has to connect an oscillator on each unit cell in order to form the
conjugated phase. Therefore, the reflection-type waveform transports along the incident way by this approach. The advantages of this antenna are that the distance between random unit cells can be the same. And it is able to modulate readily the reflected signals by modifying the operating frequency of oscillators. Nevertheless, the frequent difference between the RF and LO signals of each oscillator must be large extremely. This shortcoming will make the antenna system much complex and expensive. The antennas of Van Atta arrangement have to let each unit cell symmetrize to the central point. And two unit cells are connected by simple microwave transmission line. The framework of the antenna of Van Atta arrangement is shown in Fig. 2.2(a). The corresponding electric field in the incident direction is , where C is the constant value which has relations with the distance of a signal source and the strength of an incident waveform, N is the amount of antennas in the array and F(θ) is the pattern of each unit cell. For the sake of improving the strength of the radiating field, the transmission line can be replaced by an active amplifier, as shown in Fig. 2.2(b) and Fig. 2.2(c). The architecture in Fig.
2.2(b) only has a half of antennas in the array to receive the incident waveform due to utilizing a unilateral amplifier. This kind of antennas possesses the corresponding field
( ) θ C N F
2( ) θ E
Passive = ⋅ ⋅( )
θ C N2 G F2( )
θEUni−amp = ⋅ ⋅ ⋅ , where G is the gain of a unilateral amplifier. If the architecture adopts a bi-directional amplifier, each unit antenna can be used to receive and transmit a signal, which field is EBi−amp
( )
θ =C⋅N⋅G⋅F2( )
θ . Compared with two architectures, we can acquire a conclusion that the reflected power level of a system which adopts a bi-directional amplifier has 6dB much than the one with a unilateral amplifier. Similarly, when two antennas are designed to have the same reflected power level, the system which utilizes a bi-directional amplifier can reduce the half amount of unit antenna cells.Van Atta Array
Fig. 2.1 The principle of Van Atta Array
Antennas
l1
l2
Connecting Transmission Line
Fig. 2.2(a) Passive Van Atta retro directive array
Fig. 2.2(b) Active Van Atta retro directive array with unilateral amplifier
Antennas
l1
l2
Unilateral amplifier
Antennas
l1 l2
Bi-directional amplifier
Fig. 2.2(c) Active Van Atta retro directive array with bi-directional amplifier
2.2
m
Fig. 2.3 Transistor amplifier block diagram
2.2.1 Power Gain Equations
er gain GP, and the available power gain GA
ar
The Basic Microwave Transistor Amplifier
This section develops some basic principles used in the analysis and design of icrowave transistor amplifier. Based on the S parameters of the transistor and certain performance requirements, a systematic procedure is developed for the design of a microwave transistor amplifier.
Γs Γin Γout
The transducer power gain GT, the pow e defined as followes:
2
2.2.2 Stability Consideration
s resistance to oscillate, is a very important The stability of an amplifier, or it
co
.3 The Direct Conversion Receiver
or broadband wireless communications, wi
nsideration in a design and can be determined from the S parameters, the matching networks, and the terminations. The two-port network shown in Fig. 2.3 is said to unconditionally stable at a given frequency if the real parts for Zin and Zout are great than zero for all passive load and source impedances. If the two-port is not unconditionally stable, it is potentially unstable. That is, some passive load and source terminations can produce input and output impedances having a negative real part.
2
Because of the rapid growth in demand f
reless local area networks (WLAN) are becoming more attractive not only to exchange large amount of data locally but also as access points for the cellular infrastructure. The superheterodyne has been the architecture of choice for wireless transceivers for many years. On the other hand, due to the increase of the integration level of RF front-ends, alternative architectures, targeting reduced power consumption and minimization of the number of off-chip components, have been considered, in the recent past. Among them, the direct conversion receiver (DCR) or zero-IF receiver has increasingly gained widespread attention due to its potentially of low power consumption, lower complexity, low manufacturing costs, and easy integrating with the baseband circuits [6]-[9]. Fig. 2.4 shows the block diagram of the direct conversion RF front-end, where the LO frequency is equal (or approximate) to input carrier frequency and the LO will translate the center of the desired signal to zero IF or low IF.
RF
Filter LNA
LPF
LPF VCO
90
0
Mixer
Mixer
I
Q
Baseband ADC
Baseband ADC
I
Q
Fig. 2.4 Block diagram of direct conversion receiver architecture
The most important advantage of the direct conversion receiver is that the intermediate frequency (IF) passband filter can be neglected and replaced by a low pass filter. Low pass filter is much easier to integrate in standard semiconductor technology. However, some issues which do not exist or are not serious in the heterodyne architecture become critical in the direct conversion receiver. These drawback include DC offset, flicker noise, even order distortion, I/Q mismatch, and so on. Among these the DC offset generated by self-mixing is the most critical. The DC offset is caused by carrier leakage from the local oscillator to the mixer input and to the antenna as shown in Fig. 2.5 Interferer leakage will also cause a DC offset at the mixer output as shown in Fig. 2.6 To overcome the drawback of DC offset, the improving isolation between LO and RF ports is important. The second-order intermodulation distortion (IMD2) is a fundamental problem, because the second-order intermodulation term interferes the reception of the wanted signal as shown in Fig. 2.7. In a perfectly balanced Gilbert cell mixer, the IMD2 is a common-mode signal and therefore does not a serious problem. However, due to the mismatch of device, the balance between the negative and positive branch of the mixer is degraded and the IMD2 becomes a problem. About I/Q mismatch, if the
modulation is complex modulation, the I/Q mismatch can equal to image interferer.
This mismatches between the amplitudes of the I and Q signal corrupt the constellation of the down converted signal. Therefore influences the bit error rate.
Finally, flicker noise or l/f-noise may be a problem in the mixer and subsequent filter because the signal is converted directly to baseband.
RF
Filter LNA LPF
coswt
Mixer Baseband ADC
Fig. 2.5 LO signal leakage
RF
Filter LNA LPF
coswt
Mixer Baseband
ADC
Fig. 2.6 A strong interferer signal leakage
Desired channel
coswt
Interferer
LNA IM2 LNA IM3
Mixer IM2
Fig. 2.7 Even order distortion
2.4 Mixer Fundamentals 2.4.1 Principles of Mixer
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.
3.1 Architecture of the Bi-Directional Amplifier
A two-port bi-directional amplifier, which may simultaneously amplify the waves
coming from both ports, is proposed and demonstrated in this chapter. Fig. 3.1 shows the proposed configuration of the bi-directional amplifier, which contains two identical reflection-type amplifiers and a 3-dB quadrature hybrid [10]. The quadrature hybrid circuit can separate the input signal into two output signals with the phase difference of 90 degree and the same power level, and eliminate the signal at isolation port. The reflection-type amplifier, the device of only one end as the input and output ports, can amplify and reflect the incident signal. Port I and port II are the input and output of the bi-directional amplifier. In accordance with the principles of this circuit above, two signals produced by the quadrature hybrid circuit will be amplified by the reflection-type amplifiers and flash back to the hybrid circuit. Let a wave be incident on the bi-directional amplifier from port I as shown in Fig. 3.2, the signals with the same power and out of phase resulted at port I will cancel and the signals with the same power and the same phase resulted at port II will add. The Port I and Port II is the input and output ports of this amplifier. The role of two ports can be exchanged due to its bi-directional amplified capability. This designed process must pay attention to the oscillation condition of this circuit because its principles are similar to them of an oscillator.
Fig. 3.1 Configuration of the proposed bi-directional amplifier Reflection
-
typeamplifier
Reflection
-type
amplifierPort Ι
PortⅡ
90-degree hybrid
θ。
θ+90。
θ。
θ+90。
θ。
θ +90 。 θ+ 180 。
θ +90。
Reflection - type amplifier
Reflection - type amplifier
Port Ι
PortⅡ
90-degree hybrid
Fig. 3.2 The principle of the bi-directional amplifier
3.2 Circuit Design of the Bi-Directional Amplifier 3.2.1 Quadrature Hybrid
As shown in Fig. 3.3, the quadrature hybrid must be realized by means of transmission lines with the quarter wavelength. The length is about 8mm at the operating frequency of 5.8GHz. The transmission line is not suitable for integrated circuit implementation.
Fig. 3.3 Circuit diagram of the conventional quadrature hybrid
It is completed by adopting lump devices as shown in Fig 3.4 [11]. The symmetry of this circuit is important so that the inductors L1~L4 are using symmetric inductors provided by the standard CMOS process. Due to the lower Quality factor of the inductor implemented in integrated circuit implementation, the quadrature hybrid exhibits a through loss (S31) of 2 dB and a coupling loss (S41) of 2dB. The return loss and isolation, characterized by |S11| and |S21|, is better than 15dB as shown in Fig. 3.5(a). The phase difference between S31 and S41 is about 88∘ as shown in Fig.
3.5 (b).
Fig. 3.4 The lumped quadrature hybrid
4 5 6 7
-30 -20 -10 0
S-parameter (dB)
Frequency(GHz)
S11 S21 S31 S41
Fig. 3.5(a) The S parameters of the quadrature hybrid
C 1
L2 L1
L2 L1
Port 1 Port 2
Port 4 Port 3
4 5 6 7
phase difference (Degree)
Frequency (GHz)
S21 & S31 phase difference
Fig. 3.5(b) The phase difference between S31 and S41
3.2.2 Reflection-type Amplifier
The incident signal can be reflected and amplified by the reflection-type amplifier.
It means that the reflection coefficient Γ must be greater than one. The reflection coefficient Γ at the input port of the reflection-type amplifier is expressed as
where ZL is the input impedance of the reflection-type amplifier and Z0 is the output impedance of the quadrature hybrid. From equation (3.1), the reflection coefficient Γ will be greater than one when the input impedance ZL is negative [12]-[13]. The reflection-type amplifier is designed as shown in Fig. 3.6. And Fig. 3.7 illustrates small-signal circuit of the reflection-type amplifier. The input resistance Zin can be derived as
From (3.2), the negative resistance
f
decreasing Cf. The , resulted from MOS poly-gate, can be ignored due to multi-finger. Fig. 3.8 illustrates the simulation of input resistance.
1
r
gFig. 3.6 Schematic of the reflection-type amplifier
Fig. 3.7 Small-signal equivalent circuit model of reflection-type amplifier
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
-60 -50 -40 -30 -20 -10 0
input resistance(Ohm)
Frequency (GHz)
Real(Z(1,1)) Image(Z(1,1))
Fig. 3.8 The input resistance of reflection amplipier
Zin
C
f3.2.3 Noise Discussion
Fig. 3.10 shows the noise figure at operating frequency if the negative resistance shown in Fig 3.9 is ideal. The noise figure in Fig. 3.10 is caused by the loss of quadrature hybrid. However, there is no ideal negative resistance in practice. The negative resistance is designed as shown in Fig. 3.11. The noise figure and gain is depended on channel width. Fig. 3.12 illustrates the bi-directional amplifier noise figure increased when the channel width increase gradually. Fig. 3.13 illustrates the bi-directional amplifier gain increased when the channel width increase gradually. It means that the noise figure and gain in this design must be trade off. In order to improve the radiating filed, the focus of this design is the gain of the bi-directional amplifier.
Fig. 3.9 Bi-directional Amplifier with ideal negative resistance
4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
0 1 2 3 4 5 6 7 8 9 10
NF(dB)
Frequency (GHz) With ideal negative resistance
Fig. 3.10 The noise figure of bi-directional amplifier with ideal negative resistance
Fig. 3.11 Bi-directional Amplifier with negative resistance
Fig. 3.11 Bi-directional Amplifier with negative resistance