MPhil thesis of Lo Chi Wa - Department of Electronic & Computer ...

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“The product of Gm and Req is larger than one” where the Gm is the tranconductanceto compensate the loss in the LC tank, and Req is the equivalent parallel resistance ofLC tank at resonance. The product of Gm and Req is the loop gain at 360 o phase shift.There is another theory of LC oscillator based on negative conductance to describe theoscillation. The criterion for oscillation is “The magnitude of the negativeconductance Gm is larger than the positive conductance 1/Req”.-1/GmReqFig. 26 Model of a simple LC oscillatorBoth theories explains the oscillation but in different views. To apply these theories todetermine the oscillation amplitude and the required compensation, a generalizedcriterion can be used – “The average product of Gm and Req is larger than one” or“The average magnitude negative conductance Gm is larger than the positiveconductance 1/Req”. The region where the criterion is true determines the oscillationamplitude. The graphical representations of the criterion in the two theories are shownin Fig. 27. Based on loop gain theory, the oscillation stops when the average loop gainis smaller than one. The amplitude of oscillation will be the voltage where the loop gain(Vout/Vin) cuts the line of unity slope. Based on negative conductance, the oscillationstops when the average negative conductance ( ∫ VGmdV0 V) is smaller than thereciprocal of the resistance (1/R). The voltage (Vin=Vout when oscillation) where theaverage negative conductance cuts the reciprocal of resistance is the oscillationamplitude. Although there are different loop gains and different negative conductance40
in Fig. 27a and Fig. 27b, the same oscillation amplitude can be obtained if their averagevalues within the oscillation range are the same. As the loop gain and the negativeconductance are usually decreasing, the loop gain and the negative conductance at thecenter point have to be larger than 1 and 1/R in order to start the oscillation.aVoutVinbGmSGmdvv1/RVinFig. 27 Graphical representations of the generalized criterion for oscillation a) based on loop gain b)based on negative conductanceSurprisingly, in the most common differential LC oscillator shown in Fig. 28, thecriteria results in a very simple relationship between the amplitude of oscillation and thebias current. “The single-ended peak-to-peak amplitude of oscillation is “usually”equal to the product of the tail current in a carefully designed oscillator and theequivalent parallel resistance of one of the LC tanks at resonance.” Or therelationship can be called Ohm’s law (V=IR). “The voltage at resonance frequencyequals to the product of bias current and the equivalent resistance at resonance of theLC tank.”41
Page 1 and 2: A 1.5-V 900-Mhz Monolithic CMOSFast
Page 3 and 4: A 1.5-V 900-Mhz Monolithic CMOS Fas
Page 5 and 6: Table of ContentsPageAcknowledgment
Page 7 and 8: Testing setup......................
Page 9 and 10: List of FiguresPageFig. 1 Block dia
Page 11 and 12: Fig. 76 Amplitudes and currents of
Page 13 and 14: Chapter 1 IntroductionBackgroundWir
Page 15 and 16: applications because it can provide
Page 17 and 18: existing monolithic frequency synth
Page 19 and 20: the receiver frequency band is from
Page 21 and 22: out-of-bandin-bandout-of-band0dBmin
Page 23 and 24: Based on the maximum interference,
Page 25 and 26: carrierdBcspur∆fFig. 8 Frequency
Page 27 and 28: Spurs requirement (dBc)Frequency of
Page 29 and 30: The frequency diversity can be perf
Page 31 and 32: Chapter 3 System DesignPhase-locked
Page 33 and 34: coarse tuning can be provided by th
Page 35 and 36: array is now possible. Moreover, th
Page 37 and 38: performance of the synthesizer 9 .
Page 39 and 40: signalquantizationnoisea) f b)signa
Page 41 and 42: esolution. The loop bandwidth is 80
Page 43 and 44: the output value between 0 and 0.5,
Page 45 and 46: The coupled-LC oscillators can be v
Page 47 and 48: 890MHzf25MHz243KHz865MHzFig. 23 Tun
Page 49 and 50: onoffCwellClinearCwellClinearCwellC
Page 51: spirals of similar sizes is around
Page 55 and 56: conductance (Gm) and the reciprocal
Page 57 and 58: −19⎛ 900M⎞0.0259×1.6×10 ×
Page 59 and 60: GdoVinFig. 32 Gdo of the proposed L
Page 61 and 62: RzCzIcpCpR4C4a)IcpCzR4B.IcpCpRpC4b)
Page 63 and 64: Usually, capacitors in the filter o
Page 65 and 66: RVinFig. 38 Resistance of NMOS resi
Page 67 and 68: feedback path to prevent the proble
Page 69 and 70: 890MHz25MHz865MHzfA+∆A
Page 71 and 72: High-speed multi-modulus dividerThe
Page 73 and 74: CLKQBQDDBFig. 50 Schematic diagram
Page 75 and 76: ANDgateABclkclkclkclkQBFig. 54 Sche
Page 77 and 78: f o/2 /2,3 /2,3 /2 /2f div/4Combina
Page 79 and 80: next stage, as shown in the Fig. 59
Page 81 and 82: co10bDclkclkFig. 60 Schematic of th
Page 83 and 84: (1-Z -1 ) 23bDQBclkZ -1 (1-Z -1 )2b
Page 85 and 86: X 16clkDclkQBDclkQBFig. 66 Schemati
Page 87 and 88: ~90 oa) b) c)Fig. 68 Different meth
Page 89 and 90: (dotted line). As the oscillation c
Page 91 and 92: In practice, it is not desirable to
Page 93 and 94: and decrease in amplitude mismatch
Page 95 and 96: Current interactionThe two oscillat
Page 97 and 98: equirements. Fortunately, by connec
Page 99 and 100: LC oscillators are put apart to red
Page 101 and 102: Gain mismatch (in %)Two oscillators
Page 103 and 104:
equals to1 . By doubling the height
Page 105 and 106:
30 is obtained. It is because the s
Page 107 and 108:
The spiral inductor is designed and
Page 109 and 110:
oscillators (shown in the upper and
Page 111 and 112:
Synthesizer LayoutThe layout and th
Page 113 and 114:
Die LayoutFig. 98 shows the die pho
Page 115 and 116:
Testing setupThe testing setup show
Page 117 and 118:
Resistance (ohms)Freq (Hz)Fig. 101
Page 119 and 120:
Resistance (ohms)Freq (Hz)Fig. 105
Page 121 and 122:
VaractorFig. 109 shows the testing
Page 123 and 124:
Table 5 Summary of parameters of va
Page 125 and 126:
Table 6 Summary of N-well substrate
Page 127 and 128:
Fig. 120 Quality factor of the swit
Page 129 and 130:
The decrease in quality factor is d
Page 131 and 132:
Fig. 126 Schematic diagram of the p
Page 133 and 134:
Output frequency(MHz)Number of swit
Page 135 and 136:
Gain (MHz/V)Tuning voltage (v)Fig.
Page 137 and 138:
on the process variation. Therefore
Page 139 and 140:
voltage (Vos = Rp x Ios) appeared.
Page 141 and 142:
Although the spurs are quite large,
Page 143 and 144:
GMSK signals with 0.3 BT and a bit
Page 145 and 146:
Power spectral density (dB)(b)(a)(c
Page 147 and 148:
Summary of performanceA summary of
Page 149 and 150:
Table 10 Comparison of performances
Page 151 and 152:
As the voltage-controlled oscillato
Page 153 and 154:
Bibliography1 Thomas H. Lee, The De
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