Future Work

From chapter 2, the X-band back gate TF-QVCO could be modified as shown in Fig. 4-1. We insert a resistor between the bias transistor as current source and the core circuit [6]. Low frequency bias noise is the dominant factor for the 1/f³ phase noise.

The filtering resistance can isolate the bias transistor from the cross-coupled pair and less bias noise can be upconverted into the 1/f³ phase noise. As we increase the resistance, the 1/f² phase noise performance will reach its optimum value and begin to degrade in the same way. This is because the thermal noise contribution overwhelms the phase noise reduction by the harmonic filtering. So there is a tradeoff between 1/f² and 1/f³ phase noise performance as a function of the filtering resistance.

Fig. 4-1 Revised architecture of back gate TF-QVCO

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Appendix

CMOS Low-Noise Amplifier for UWB System

A.1 Introduction

A low-noise amplifier is the first stage in the receiver block of a communication system. For UWB applications, the criteria to judge its performances are slightly different from narrow system. Because transmitted power spreads over a wide range and is restricted to be less than -41.3 dBm per MHz, the requirement on linearity in UWB system is not such important as in narrow system. The important requirements for UWB applications are wide-band input impedance matching, low power consumption, low noise performance, and enough gain to suppress noise of the next stages.

Fig. A-1 shows the four basic 50 Ohm input matching techniques. However, these topologies have some drawbacks. The four input matching is only suit for narrow band amplifier [26][27][28][29][30].

(a) (b)

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(c) (d)

Fig. A-1 Basic input matching topology. (a) Inductive source degeneration.(b) Direct resistor termination.(c) Shunt-series feedback.(d) Chebyshev band-pass filter Fig. A-1 (a) is traditional source degeneration topology, because it only resonances at one frequency, it can’t achieve wide-band 50 Ohm matching. It realizes only narrow band matching. Fig. A-1 (b) is the resistive termination matching, because of the loading effect, it will loss a lot of voltage if resistive termination matching is used. Fig.

A-1 (c) is feedback method. It can achieve wideband input matching. But because of feedback mechanism, it can’t achieve high gain to suppress noise of the next stages. Fig.

A-1 (d) is LC 3’rd Chebyshev band-pass filter. It can perform good input matching, but it consumes large chip area because of using four inductors for input matching.

The noise performance of an LNA is directly dependent on its input matching.

The wide-band input matching is intrinsically noisier than narrow-band counterparts as the noise performance can not be optimized for a specific frequency. Thus the designer has to be trade off between the input matching and noise.

Distributed amplifiers [31]

The Fig. A-2 shows a basic four-stage single-ended distributed amplifier.

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Fig. A-2 Basic four single-end distributed amplifier

The distributed amplifiers normally provide wide bandwidth characteristics but they consume large dc current due to the distribution of multiple amplifying stages, which make them unsuitable for low-power application. And the distributed amplifiers are not optimized for noise. This bring the challenge of finding a low-power topology that satisfies all the other design requirements, the most stringent one being the input match.

Ultra-wideband low noise amplifier using LC-ladder filter input matching network [32][33]

Recently another topology of wideband LNA has been present. It expands the conventional narrow-band LNA using source degeneration by embedding the input network of the amplifying device in a multisection reactive network so that the overall input reactance is resonated over a wider bandwidth. Fig. A-3 shows a typical narrowband cascode LNA topology and its small-signal equivalent circuit.

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Fig. A-3 Narrowband LNA topology. (a) overall schematic. (b) Small-signal equivalent circuit at the input

The inductor L_s is added for simultaneous noise and input matching and L_g for the impedance matching between the source resistance Rs and the input of the narrowband LNA [14]. Fig. A-3(b) shows the equivalent small-signal circuit. Assume the gate-drain Cgd can be ignored, the impedance of the gate terminal is a series RLC circuit. The reactive part of the input impedance is resonated at the carrier frequency in narrowband design. The basic concept of the LC-ladder input matching is expanded from the input impedance of the narrowband which is a series RLC circuit. Consider a fourth-order bandpass ladder filter, shown as in Fig. A-4.

Fig. A-4 Fourth-order bandpass ladder filter used for impedance matching.

The right part of the bandpass filter looks similar to the equivalent circuit of the inductively degenerated transistor in Fig. A-3(b). Therefore, the bandpass filter can embed the inductively degenerated transistor and obtain the desire input impedance.

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The LC-ladder filter input matching of wideband LNA has two significant drawbacks.

Because the LC-ladder filter at the input mandates a number of reactive elements, which could lead to a larger chip area and noise figure degradation in the case of on-chip implementation.

Ultra-wideband low noise amplifier using the common-gate as the first stage.[34]

In traditional narrow-band receiver the common-gate is not used widely due to its relatively lower gain and higher noise figure than a common-source amplifier. The actual configuration of common-gate stage is shown in Fig. A-5(a).

Fig. A-5 (a) Configuration of a common-gate input stage.

(b) The small-signal equivalent circuit.

From the Fig. A-5(b), we can derive the input impedance

) frequency band of interest.

)

After some mathematical calculation

- 61 - relatively constant within the 3.1-10.6GHz UWB band. The imperfect matching of the common-gate stage throughout the band arise from the frequency dependent Xs(ω) that dominates the imaginary part in the denominator. To get a good matching over the wide band , the LC tank of Xs(ω) formed by Ls and C_gs should be selected such that they resonate at the center of the 3.1-10.6GHz, leaving only a 50Ω real input impedance. The noise figure of the common-gate input stage UWB LNA can be improved by increasing gm1 but it will degrade the input matching.

Wideband matching using the transistor intrinsic gate-drain capacitor [35]

Recently a novel wideband input match has been present. It considers the gate-drain capacitor has significant effect on the circuit performance. The Fig. A-6 show a simple common source amplifier with source degeneration inductor and the drain loaded an equivalent capacitor and resistor from the next stage.

Fig. A-6 The small signal equivalent circuit of common-source with inductive source degeneration

The Cgd and ro are neglected in conventional analysis of low noise amplifier. It is inaccurate numerically. If both C_gd and r_o are considered we will find that the input match at high frequency is depend on the resistive load and at low frequency is depend on the capacitive load. We can achieve wideband match without external input

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match network. It also can achieve low noise match. Therefore, we will adopt this wideband matching method as a part of the proposed LNA.