Chapter 5 Conclusions
A low power and low phase noise dual-band LC-VCO operating at 2.5 GHz and 3.5 GHz is proposed and implemented by TSMC 0.18-μm 1P6M CMOS process. The design uses the current-reused topology combined with an external-added resistor at the substrate node of the NMOS to achieve low power and low phase noise. With the current-reused topology, the proposed LC-VCO can operate using only half amount of DC current compared with the conventional topologies. The external resistor reduces the thermal noise of the NMOS and the reduction of the thermal noise decreases the phase noise of the LC-VCO effectively. The proposed LC-VCO consumes 3.12 mW and 3.64 mW at 2.5 GHz and 3.5 GHz, respectively. The measured phase noise at 1 MHz offset frequency is -121 dBc/Hz and -117 dBc/Hz in the 2.5 GHz and 3.5 GHz.
Generally, the FoM of dual-band LC-VCO is -178 dBc/Hz at 1MHz offset frequency.
The FoM of proposed LC-VCO is -184 dBc/Hz and -183 dBc/Hz at operating frequency 2.5 GHz and 3.5 GHz, respectively. Although the power consumption is obviously improved, there is still a lot of space for noise reduction. Several extensive studies have been underway to further reduce phase noise of LC-VCOs. In this field, it maybe worth our effort in the future works, such as low phase noise LC-VCOs.
References
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Appendix A Basic Oscillator Theory
Appendix A Basic Oscillator Theory
The oscillator is an energy transfer device which is able to transfer DC power to AC power. The two methods to analysis the oscillator are Barkhausen’s criteria [7]
and negative resistance. The core of oscillator circuit is a loop that causes a positive feedback at a selected frequency as shown in Figure A.1. In this closed-loop feedback system, the oscillated condition can be established by combining the transfer functions of the active circuit HA(S) with the feedback stage HF(S) to the closed-loop transfer function as follow
( ) ( ) ( )
1
out A
in F A
H s
V
V = H s H s
− (A-1)
Figure A.1 The block diagram of closed-loop feedback system.
Appendix A Basic Oscillator Theory
The denominator of the transfer function must become zero at the frequency of interest for a self-sustaining oscillation. Thus, S = jω0, HF
(
jω0)
⋅HA(
jω0)
= +1, then the closed-loop gain approaches infinity at ω0 . The small signal whose frequency makes the above situation happen will be unlimitedly amplified by the circuit every cycle. Therefore, the oscillation happens.For steady oscillation, two conditions must be simultaneously met at the oscillation frequencyω0. Both of the equations are called as Barkhausen’s criteria.
The above conditions imply that any feedback system can oscillate if its loop gain and phase shift are chosen properly.
(
0) (
0)
1 For example, Figure A.2 shows the ring oscillator which is cascade of N stages with an odd number of inverters is placed in a feedback loop. We suppose that the gain of every inverter is A0 and the inverter has only one poleω0. The transfer function of the ring oscillator is given by0
From equation (2-4), we can know that 180°of phase shift is proved by the chain of N stages, each stage must provide 180
N
° of phase shift sufficient gain atω0.
Therefore, the oscillation frequency is
1
Appendix A Basic Oscillator Theory
From (2-5) and (2-6), the gain of every inverter is calculated by
2
Figure A.2 Schematic of the ring oscillator.
In fact, the gain of every inverter is 2-3 times the proportions of A0, because it ensures that the ring oscillator operates normally. The ring oscillator is analyzed effectively by Barkhausen’s criteria. However, the LC-tank oscillator can be analyzed easily by negative resistance analysis.
The negative resistance analysis is developed to design the oscillator [8]. The canonical RF circuit for a one-port negative-resistance oscillator is shown in Figure A.3. The input impedance of the active device is Zin =Rin+ jXin, and the device is terminated with a passive load impedance, ZL =RL+ jXL.
Appendix A Basic Oscillator Theory
Figure A.3 Schematic diagram of the one-port negative-resistance oscillator.
Applying Kirchhoff’s voltage law gives
(Zin+ZL)I = (A-8) 0 When oscillation is occurring, the RF current I is nonzero. The following conditions must be satisfied：
in L 0
R +R = , (A-9)
in L 0
X +X = . (A-10) From the equation (A-5), while a positive resistance ( RL > ) implies energy 0 dissipation, a negative resistance (Rin < ) implies and energy source. The condition 0 of (A-6) controls the frequency of oscillation. For the steady-state oscillation condition,Zin+ZL = , implies that the reflection coefficients 0 Γ and L Γ are in Thus, for steady-state oscillation, the condition of Γ ⋅Γ = must be satisfied. L in 1
At the higher operating frequency, the S-parameters are usually used to design oscillators. Hence, the two-port analysis is needed in the transistor oscillator design, and the circuit model is shown in Figure A.4. A negative-resistance one-port network is created by terminating a potentially unstable transistor with and impedance designed to drive the device in an unstable region.
Appendix A Basic Oscillator Theory
Figure A.4 Schematic diagram of the two-port negative-resistance oscillator.
For the oscillator design, the positive feedback is used on active device to enhance the instability of the device. The output stability circuit can be drawn in the Γ plane, and T Γ is selected to produce a large value of negative resistance at the T From the equation (A-7), the input reflection coefficient is
12 21 11 Also, the output reflection coefficient is
12 21 22 From equations (A-11) and (A-12) it follows that
Appendix A Basic Oscillator Theory
T out 1
Γ Γ = (A-17) andZT = −Zout. Therefore, the condition for oscillation of the terminating network is satisfied.
LC-tank VCO is using negative resistance of active circuit to cancel the resistance of LC-tank as shown in Figure A.5 [9]. The series transfers to parallel as shown in Figure A.6. Figure A.7 shows the equivalent resonant model. The LC-tank oscillator is also called the negative-Gm oscillator.
Figure A.5 Negative resistance and LC-tank resistance.
Figure A.6 Series to parallel.
Figure A.7 Equivalent resonant model.
Appendix A Basic Oscillator Theory
The negative resistance is produced from cross-coupled pair which is positive feedback. The impedance seen at the drain of M1 and M2 can be calculated which is
in 2
m
R =− g as shown in Figure A.8. In general, the phase noise of PMOS-corss coupled pair is lower than NMOS-cross coupled pair.
Figure A.8 Input impedance of NMOS cross-coupled pair.
Appendix B Classifications of Noises
Appendix B Classifications of Noises
The noise sources remained mysterious until H. Nyquist, J. B. Johnson and W.
Schottky published a series of papers that explained where the noise comes from and how to expect it [17]. The sensitivity of communications systems is limited by noise, because it does no separate, suppose, artificial noise sources from more fundamental sources of noise. We have to understand the theorem of noise, and we can improve the noise performance of RF circuits.
B.1 Thermal Noise of Resistor
As shown in Figure B.1, the thermal noise of a resistor R can be modeled by a series voltage source. The mean-square open-circuit noise voltage is therefore
2
4
V
n= kTR f Δ
(B-1) Where k is the Boltzmann’s constant that is 1.38×10−23 J/K, T is the absolute temperature in kelvins, and fΔ is the noise bandwidth in hertz over which the measurement is made.Appendix B Classifications of Noises
Figure B.1 The thermal noise model of resistor.
B.2 Thermal Noise in MOS
Since metal-oxide-silicon (MOS) is essentially voltage-controlled resistors, it exhibit thermal noise. In the triode region of operation particularly, one would expect noise proportional to the resistance value. The thermal noise mainly includes the drain current noise, the gate noise, the substrate noise, etc.
A. Drain Current Noise
The drain current noise model of MOS is shown in Figure B.2. It can be modeled by a current source connected between the drain and source terminals with a spectral density：
2
4 0
nd d
I = kT g
γ
Δf (B-2)Where gd0 is the drain-source conductance at zeroVDS. The parameterγ that has a value of unity at zeroVDSin long devices decreases toward a value of 2/3 in saturation region. Unfortunately, measurements show that short channel NMOS devices in saturation exhibit noise far in excess of values predicted by long-channel theory, sometimes by large factors.
Appendix B Classifications of Noises
Figure B.2 The drain current noise model of MOS transistor.
B. Gate and Substrate Noise
In addition to drain current noise, the ohmic sections of a MOS also contribute thermal noise. The gate, source, and drain materials exhibit finite resistivity, thereby introducing noise. For a relatively wide transistor, the source and drain resistance is typically negligible, but the gate distributed resistance may become noticeable. The contribution to the effective gate resistance is not only from the physical gate electrode resistance but also from the distributed channel resistance as shown in figure B.3 [18]. In the noise model of figure B.4, a lumped resistor Rg represents the distributed gate resistance and the noise source is modeled by a series voltage source.
The gate noise can be expressed as
2
4
ng g
V = kT R δ Δ f
(B-3) Theδ is the coefficient of gate noise, classically equal to1.33 for long-channel device. Although the noise behavior of long channel devices if fairly well understood, the precise behavior ofδ in the short channel regime is unknown at present, it is probably reasonable as a crude approximation to assume thatδ continues to be aboutAppendix B Classifications of Noises
twice as large asγ . Hence, γ is typically 2-3 for short channel NMOS devices, δ may be taken as 4-6. The gate distributed resistance is given by：
3
2 H gR R W
= n L
(B-4) Where RH is the sheet resistance of the poly-silicon, W is the total gate width of the device, L is the gate length of the device, and n is the number of gate fingers used to layout the device.Figure B.3 Equivalent gate resistance consists of gate poly and channel.
Figure B.4 The gate noise model of MOS transistor.
Appendix B Classifications of Noises
The material of substrate also exhibit finite resistivity, so the thermal noise of substrate in the MOS can be expressed as：
2
,
4
n sub sub
V = kTR Δ f
(B-5) WhereRsubis the resistor in the substrate of the MOS transistor. The equivalent noise voltage of this resistor modulated the back gate, producing a mean-square drain noise current component whose value is given by2 2
,
4
n sub sub mb
I = kTR g Δ f
(B-6)g
mb is the parameter that is caused by body effect.C. Induced Gate Current Noise
At high-frequency, the local channel voltage fluctuations due to thermal noise couple to the gate through the oxide capacitance and cause an induced gate noise current to flow. Figure B.5 shows the induced gate current noise and its small signal model in the MOS transistor. A simple gate circuit model that includes both of a shunt noise current ig2 and a shunt conductance gg have been added. Mathematical expressions for these sources are are given by:
2
Figure B.5 Induced gate current noise and small signal model in MOS transistor.
Appendix B Classifications of Noises
D. The Correlation between Drain Noise and Induced Gate Noise
From Figure B.5, the drain noise and induced gate noise share a common physical origin and it is expressed by cross-correlation between the two noise.
0 The cross-correlation coefficient is defined as equation (9) and is about 0.395j in MOS device:
For the noise analysis, the induced gate noise can be split into two components.
The first one is fully uncorrelated with the drain noise, and the other is fully correlated with the drain noise. It can be written as:
2 2
2 4 (1 ) 4
g g g
i = kT gς − c Δ +f kT g cς Δf (B-12) The correlation noise circuit for RF MOS transistor is shown in Figure B.6.
Figure B.6 The correlation noise circuit for RF MOS transistor.
Appendix B Classifications of Noises
Appendix B Classifications of Noises