Thesis Organization - 利用順向基極偏壓設計之低功耗低雜訊放大器

Chapter 1 Introduction

1.2 Thesis Organization

This thesis presents the work on the design and implementation of ultra-low power LNAs for receiver front-end circuits. The main objective of this thesis is to develop ultra-low power LNA design methods and certify the proposed topologies using RF CMOS processes.

The contents consist of two major topics, such as “low-power UWB LNA design for 3.1~10.6 GHz wireless receivers” and “sub-0.2mW ultra-low power LNA for wireless body area network (WBAN) sensors.

In Chapter 2, we will introduce the basic concepts of LNAs design. Some conventional LNA input matching architecture will be discussed, and MOSFET noise model and the theoretical background will be addressed. Furthermore, dynamic threshold voltage CMOS technique (by using body biases) is also covered in this chapter.

In Chapter 3, we will present the design and implementation of a low-power LNA for

3.1~10.6 GHz UWB applications. We will discuss the circuit topology, the method for wideband input/output matching, and for the optimization of gain as well as noise. The test chip of LNA was fabricated by TSMC 0.13μm 1P8M CMOS Mixed Signal RF General Purpose Standard Process. The Si data measured from the test chip will be analyzed and compared with what predicted by simulation.

In Chapter 4, a narrow band LNA intended for application in 1.4 GHz WBAN is introduced. The details of circuit design and analysis method will be presented. This ultra-low power LNA chip was fabricated by UMC 90nm low leakage (logic and mixed-Mode 1P9M low-k) process. The measured results will be compared with the predicted performance from ADS simulation to verify the proposed circuit topology for ultra-low power, the root causes responsible for deviation from simulation, and the improvement solutions. In Chapter 5, conclusions are made and some critical points are proposed as the future work.

Chapter 2 Basic Concepts of Low Noise Amplifier Design

2.1 Conventional LNA Input Matching Architecture

Low noise amplifier is the first stage in the receiver front-end circuits and is used to amplify the received weak RF signal with the minimum noise figure. As it is well recognized that impedance matching is the fundamental requirement in LNA designs for achieving the target performance of both gain and noise. There are four basic 50-Ω input matching architectures that have been explored in the traditional transistor-amplifier shown in Fig. 2.1.

In this section, we will have a review and discussion on the mentioned matching circuit architectures that can be used in LNA design [3, 4].

Fig. 2. 1 Traditional transistor-amplifier of input matching

2.1.1 Resistive Termination Architecture [3]

Resistive termination architecture is the most straightforward approach to providing a reasonably broadband 50-Ω termination. It is simply to put a 50-Ω resistor (R1) across the input terminals of the LNA as shown in Fig. 2.2.

The bandwidth of this matching technique is determined by the input capacitance Cgs of the transistor M1 and can be very high. Unfortunately, the resistor R1 adds thermal noise of

its own and so attenuates the signal (by a factor of 2) ahead of the transistor. The combination of these two effects generally produces unacceptably high noise figures. More formally, it is straightforward to establish the lower bound on the noise figure of this circuit, given by (2-1) [3]:

4 1

NF g R

≥ + α ⋅ (2-1) where

0 m d

α g and γ is the coefficient of channel thermal noise, and R_s =R₁= . For R long-channel devices, ²

γ = 3 and α= . This bound applies only in the low-frequency limit 1 and ignores gate current noise altogether. Naturally, the noise figure is worse at higher frequencies and when gate noise is taken into account. Hence, the resistor termination technique is not practical in most application.

Fig. 2. 2 Resistive termination matching technique

2.1.2 Inductive Source Degeneration Architecture [3]

The inductive source degeneration architecture shown in Fig. 2.3 is popular with input matching technique of LNA. [4-18]. An important advantage of this method is that one then has control over the value of the real part of the impedance through choice of inductance, as is clear from computing the input resistance through a circuit analysis on the inductive source degeneration architecture in Fig. 2.3 and the resulted equivalent circuit in Fig. 2.4. This

method does not introduce additional noise (as in the case of using a shunt input resistor) and doesn’t restrict the value of gm (as in the case of the common-gate configuration).

To simplify the analysis, consider a device model that includes only a transconductance and a gate-source capacitance Cgs. The impedance looking through the gate inductor can be written as: From (2-2), in order to achieve an input impedance matching, the following condition must be satisfied: according to the following condition:

At the resonance frequency where the imaginary part of impedance, i.e. the reactance contributed from the inductors (L and_s L_g) and capacitor C_gs are canceled out, the input impedance is left with just the first term in (2-2), i.e. the resistance representing the real part of impedance.

Fig. 2. 3 Inductive source degeneration matching technique

L

ω

Fig. 2. 4 Equivalent circuit of inductive source degeneration matching

Note that the form of (2-2) clearly shows that the input impedance is purely resistive at only one frequency (at resonance), however, so this method can provide only a narrowband impedance matching.

2.1.3 Shunt-Series Resistor Feedback Architecture [3]

The shunt-series resistor feedback architecture as shown in Fig. 2.5 can provide good wideband matching and flat gain, but tends to suffer from poor noise figure (NF) and large power dissipation. [11, 19-23]

The impedance Zin can be written as RFM. The resistor

F FM

R R

= A

− represents the Miller equivalent input resistance of RF, where Av is the open-loop voltage gain (A_v ≈g R_m₁ _L). We design 50R_FM =R_s = Ω to achieve a matching to 50-Ω. The architecture as shown in Fig.

2.5 suffers from fewer problem than the architecture as shown in Fig. 2.2, yet the resistive feedback network continues to generate thermal noise of its own and also fails to present to the transistor an impedance that equals Zopt at all frequencies. As a consequence, the overall amplifier’s noise figure, while usually much better than that of Fig. 2.2.

In the resistive shunt-feedback amplifier, input resistance is determined by the feedback resistance (RF) divided by the loop-gain of the feedback amplifier. Therefore, the feedback resistor tends to be a few hundred ohms in order to match the low signal source resistance of typically 50-Ω. This inappropriately large resistance generally leads to significant NF degradation. Furthermore, even with a moderate amount of voltage gain, the amplifier requires a rather large amount of current, especially in the CMOS, due to its strong dependence on the voltage gain from the transconductance of the amplifying transistor M1.

[15] As a consequence, it will consume higher power dissipation and require good quality on-chip resistors for achieving a precise feedback resistance.

Fig. 2. 5 Shunt-series resistor feedback matching technique

2.1.4 Common-Gate Input Architecture (1/gm termination) [3]

The last input matching method for realizing resistive input impedance is to use a common-gate input architecture shown in Fig. 2.6. Since the resistance looking into the

source terminal is 1/gm, a proper selection of device size and bias current can provide the desired 50-Ω resistance. Using the common-gate input architecture, the minimal NF which can be achieved at low frequencies and neglecting gate current noise is NF 1 γ 2.2dB

≈ +α ≥ where

0 m d

α g and γ is the coefficient of channel thermal noise. Note that for long channel devices, NF=2.2 dB corresponding to α = 1 and γ = 2/3. As for short channel devices

( 1, ²

α ≤ γ ≥ 3), NF perhaps as high as 4.8 dB ( γ 2

α ⁼ ). The noise figure will become significantly worse at higher frequencies and when gate current noise is taken into account.

Fig. 2. 6 Common gate input matching technique

As compared to the conventionally used common-source topology, the common-gate input architecture is an efficient way to achieve a broadband matching with small chip area.

Because it doesn’t need many inductors to achieve wideband input matching. However, it can’t provide sufficient gain and lower noise figure with low power consumption [24].

2.1.5 LNA design and Comparison of Input Matching Architecture

For LNA design, the trade-offs between the gain, noise, and power consumption are critical factors to be considered for the selection of circuit topologies, impedance matching methods, and details to the active and passive devices design. In the following, the major

requirements and trade-offs are described, tentatively as a design guideline.

1) Low power dissipation :

In general, low power RF circuit design is challenging, due to trade-off between gain, linearity, and noise, etc. For a broadband LNA design, the power dissipation becomes even worse and makes low power design more difficult in the broadband circuits.

2) Input and Output matching (return loss)

In wireless receiver, the components placed in front of LNA are usually filter and antenna with the characteristic impedance 50-Ω, so input impedance matching of LNA must realize a match to 50-Ω. Unfortunately, the architecture for an input impedance matching is always different from that for an optimum noise matching.

3) High power gain

For LNA design, power gain is one of the most important performance parameters to be considered. Power gain should be sufficiently high to amplify the small RF signal from the receiver and then reduce the noise generated from the following stages. However, the larger power gain will generally degrade the linearity in LNAs.

4) Low Noise Figure (NF):

As it is well known that LNA acting as the amplifier in a receiver system, the noise generated from itself dominates the noise from all other components following the LNA.

Thus, minimizing noise figure (NF) becomes the most important target in LNA design. As a matter of fact, the optimization of NF is sometime traded off with power gain and power dissipation.

The benchmark of various input matching methods as mentioned is summarized in Table 2.1.

Table 2. 1 Comparison of LNA Input matching architectures Input matching architectures Advantages Drawbacks

Favorable for wideband input matching.

Good power gain.

Good linearity.

Higher noise figure

(extra thermal noise from the resistor).

Suitable for narrow band input matching.

Good noise performance.

Good power gain.

Good linearity.

Limited to narrow band.

Large area consumed by on-chip inductors

Suitable for wideband input matching.

Good linearity.

Good reverse isolation.

Lower power gain.

Higher noise figure.

2.2 C hebyshev Filter [25, 26]

Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple or stopband ripple than Butterworth filters. Chebyshev filters have the property that they minimize the error between the idealized filter characteristic and the actual over the range of the filter, but with ripples in the passband. This type of filter is named in honor of Pafnuty Chebyshev because their mathematical characteristics are derived from Chebyshev polynomials.

Because of the passband ripple inherent in Chebyshev filters, filters which have a smoother response in the passband but a more irregular response in the stopband are preferred for some applications.

2.2.1 Theory of Chebyshev Filter [25, 26]

The gain (or amplitude) response as a function of angular frequency ω of the nth order low pass filter is

2 2

where ε is the ripple factor, ω0 is the cutoff frequency and Tn( ) is a Chebyshev polynomial of the nth order.

The passband exhibits equiripple behavior, with the ripple determined by the ripple factor ε. In the passband, the Chebyshev polynomial alternates between 0 and 1 so the filter gain will alternate between maxima at G= and minima at 1

1 G 1

= ε

+ . At the cutoff frequency ω0 the gain again has the value

1+ε but continues to drop into the stop band as the frequency increases. This behavior is shown in the diagram on the Fig. 2.7.

Fig. 2. 7 The frequency response of a fourth-order Chebyshev low-pass filter with ε = 1 The order of a Chebyshev filter is equal to the number of reactive components (for example, inductors) needed to realize the filter using analog electronics.

The ripple is often given in dB:

Ripple in dB =

20log 1

1+ε (2-6) so that a ripple amplitude of 3 dB results from ε = . 1

a. Poles and zeroes

For simplicity, assume that the cutoff frequency is equal to unity. The poles (ωpm) of the gain of the Chebyshev filter will be the zeroes of the denominator of the gain. Using the complex frequency s:

2 2

1+ε T_n (−js) 0= (2-7) Defining − =js cos( )θ and using the trigonometric definition of the Chebyshev polynomials yields:

2 2 2 2

1+ε T_n (cos( )) 1θ = +ε cos ( ) 0nθ = (2-8) Solving for θ

1arccos( j) m

n n

θ π

= ± + (2-9)

where the multiple values of the arc cosine function are made explicit using the integer index

m. The poles of the Chebyshev gain function are then:

cos( ) cos( arccos(1 ) )

Using the properties of the trigonometric and hyperbolic functions, this may be written in explicitly complex form:

This may be viewed as an equation parametric in θn and it demonstrates that the poles lie on

an ellipse in s-space centered at s = 0 with a real semi-axis of length

sinh( )1

sinh( )

ar n

ε _{and an}

imaginary semi-axis of length of

sinh( )1

cosh( )

ar n

ε _.

2.2.2 Applications of Chebyshev Filter [27]

Filters are signal-processing circuits used to modify the frequency spectrum of an electrical signal. They may be used to amplify, attenuate, or reject a certain range of frequencies of their input signals. Filters are pervasive in integrated circuits because of their vast number of applications. Some applications include noise reduction in communication systems, band-limiting of signals before sampling them, conversion of sampled signals into continuous-time signals, signal demodulation, improving the sound quality of audio system components such as loudspeakers and receivers, and many others.

The Chebyshev response is a mathematical strategy for achieving a faster roll-off by allowing ripple in the frequency response. Analog and digital filters that use this approach are called Chebyshev filters. For instance, analog Chebyshev filters were used for analog-to-digital and digital-to-analog conversion.

The Chebyshev gives a much steeper roll-off, but passband ripple makes it unsuitable for audio systems. It is superior for applications in which the passband includes only one frequency of interest (e.g., the derivation of a sine wave from a square wave, by filtering out the harmonics).

2.3 linearity [28]

Linearity is one of the key requirements in LNA design to maintain linear operation in the presence of a large interfering signal and when the input is driven by a large signal. Any nonlinear transfer function can be mathematically written as a series expansion of power-law terms unless the system contains memory. The input V_i and output V_o of a two-port network can be related by a power series. For simplicity, we make an approximation to the third order term:

2.3.1 Harmonic Distortion [28]

If a sinusoidal waveform is applied to a nonlinear system, the output generally exhibits frequency dependent components that are integer multiples of the input frequency. In (2-12), setting V t_i( )=Acos( )ωt , then

In (2-13.1), the term with the input frequency ω is called the “fundamental” and the higher-order terms the “harmonics”. The first term in (2-13.1) is the linear term and is the ideal output if the two-port network is completely linear. Other terms in (2-13.1) are responsible for nonlinearities, and they cause a DC shift as well as distortion at frequencies

2ω , 3ω , and higher harmonics derived in (2-13.2), which result in either gain compression or gain expansion. It can be observed from (2-13.2) that distortion is present in any signal level.

2.3.2 1-dB Compression Point (P1dB) [28]

In most circuits of interest, the output is a “compressive” or “saturating” function of the input; that is, the gain approaches zero for sufficiently high input levels. In (2-13) this occurs if α₃ < . Written as 0 ₁ 3 ³ ³

4 A α A

α + , α₁A represents the fundamental amplitude and the gain

is therefore a decreasing function of the third-order harmonic proportional to

α

₃A³. In RF circuits, this effect is quantified by the “1-dB compression point”, defined as the input signal level that causes the small-signal gain to drop by 1 dB. As shown in Fig. 2.8, which is plotted on a log-log scale as a function of the input level, the output level falls below its ideal value by 1 dB at the 1-dB compression point [28].

Fig. 2. 8 Definition of the 1-dB compression point To calculate the 1-dB compression point, we can write from (2-13.3)

2.3.3 Intermodulation [28]

Harmonic distortion that was introduced previously is the result of nonlinearities due to a single sinusoidal input. When two signals with different frequencies are applied to a nonlinear system, the output in general exhibits some components that are not harmonics of the input frequencies. Called intermodulation (IM), this phenomenon arises from “mixing”

(multiplication) of the two signals when their sum is raised to a power greater than unity. To investigate the effects of both harmonic distortion and intermodulation, we assume that the input signal is composed of two different frequencies ω and ₁ ω given in (2-16) 2

1 1 2 2

( ) cos( ) cos( )

V ti =A ωt +A ωt (2-16) (2-16) can be substituted into (2-12). Thus, the output can be expressed as

Expanding the right-hand side and discarding the dc terms and harmonics, we obtain intermodulation products expressed in (2-18) and (2-19) for the second order and (2-20) for the third order IM products, namely IM2 and IM3.

1 2: 2 1 2A A cos[( 1 2) ]t 2 1 2A A cos[( 1 2) ]t

and the fundamental components written in (2-21)

3 2 Fig. 2.9 in which the input RF signals are two-tone with two different frequencies such as

ω and 1 ω 2

Fig. 2. 9 Intermodulation in a nonlinear system where it is assumed that A₁= A₂ = . A

From Fig. 2.9, it is apparent that the third-order intermodulation distortion IM3 signals are close to the signals of interest F, which makes the filtering out of IM3 signals difficult when recovering the signals of interest. Therefore minimizing intermodulation distortion is a key objective in many RF circuit design.

2.3.4 Third-Order Intercept Point (IIP3) [28]

From (2-17)~(2-21) and let A₁= A₂ = , we can drive the expression A increase proportional to A , whereas if the input level A increases to the intercept point so that ₁ 9 ₃ ²

| |

α >>4 α A is no longer valid, the gain will drop and the third-order IM products in proportion to A³ will take over the fundamentals, as shown in Fig. 2.10(a). Plotted on a logarithmic scale [Fig. 2.10(b)], the magnitude of the IM products grows at three times the rate at which the main components increase. The third-order intercept point, namely IP3 is defined to be at the intersection of the two lines. The horizontal coordinate of this point is called the input IP3 (IIP3), and the vertical coordinate is called the output IP3 (OIP3).

(a) (b)

Fig. 2. 10 (a) The linear gain and the nonlinear component (b) The IIP3 and OIP3

If ₁ ⁹ ₃ ²

One more important consideration for an amplifier design like LNA is the assurance of stability. For LNAs in the form of a two-port network, the requirement for ensuring stability is that it must not produce an output with oscillatory behavior. The stability of a two-port network can be determined from the S-parameters, the matching networks, and the terminations. Simpler tests can be used to determine unconditional stability [29]. One of these is the K-△ test, where it can be shown that a device will be unconditionally stable if Rollet’s condition [30], defined as

2 2 2

along with the auxiliary condition that

11 22 12 21 1

S S S S

Δ = − < (2-26) are simultaneously satisfied. These two conditions are necessary and sufficient for unconditional stability.

While the K-△ test of (2-25)~(2-26) is a mathematically rigorous condition for unconditional stability, it cannot be used to compare the relative stability of two or more devices since it involves constraints on two separate parameters. However, a new criterion has been proposed [31] that combines the S parameters in a test involving only a single parameter, μ, defined as Thus, if μ >1, the device is unconditionally stable. In addition, it can be said that larger values of μ implies greater stability.

2.5 Noise in Two-Port System [3]

2.5.1 Noise Factor

Noise factor (F) is defined as the signal-to-noise power ratio at the input to the signal-to-noise power ratio at the output. Considering a network with gain G and noise Na, noise factor then can be express as (2-28) [3]

/ / @

Generally we use this measure in the unit of dB, namly noise figure (NF) written in (2-29) 10 log

NF = F (2-29) A useful measure of the noise performance of a system is the noise factor, denoted as F

and given in (2-28). To define it and understand why it is useful, consider a noisy (but linear) two-port network driven by a source that has an impedance Z_s and an equivalent series noise

voltage e , illustrated in Fig. 2.11. _s²

If we are concerned only with overall input-output behavior, it is an unnecessary

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