Prediction Method of Phase Noise

4.5.1 Prediction of Phase Noise

Phase noise prediction of the integrated LC voltage-controlled oscillators (VCOs) is an interesting topic of research. A general method is proposed which is capable of making an effective prediction of F, device excess noise number, and acquiring the phase noise of oscillators accurately.

Integrated LC VCOs are common functional blocks in modern wireless communication systems and are used as local oscillators to convert up or down the RF signals. Phase noise of the VCO is one of the important issues regarding to the receiving quality. Active device noise usually contributes a significant portion to phase noise in the oscillator. It is well known that, from the Leeson’s model, the single-side power spectral density is given by Eq. (4.1). Recently, the phase noise behaviors are studied by many authors [11.34.40.45]. In this study, the method of predicting the excess noise number is indicated.

Actually, the factor F is attributed from two parts, one is the total noise sources NF in all active devices, and the other is from the mixing mechanism in oscillation under large-signal operation. The former one is closely related to the noise figure of each device. If the multiplication factor is denoted as Km, then the excess noise number F can be given by[42]

F(dB)= NF +Km (4.19)

The total noise voltage density far from the corner frequency appeared at one of the output drain in the cross-coupled oscillator is given by

k

where g is the transconductance of transistor[4] and_m γ is 2~3 for short channel effect due to hot-electron [7]. The subject index n or p is the nMOS or pMOS, respectively.

The first two terms are from active deices. Because of the symmetry, the noise level is twice. The third one is attributed from the equivalent parallel tank conductance

g

_tankcaused by ohmic losses in the metal and substrate. Then the total device noise figure, NF , is calculated from

50 ) predicted by Eq. (4.19). The upconversion factor Km is 4dB in our case of optimum

situation. It may be higher value move than 10 dB from the worst case.

4.5.2 Phase Noise Minimization

As indicated in [35], the smaller

L

²

g

_L²/

I

_bias is, the better phase noise is. When the inductance decreases, the equivalent parallel conductance of spiral inductor

g

_Lis larger but L²g_L²is smaller, which is shown in Fig. 4.14(a) and Fig. 4.14(b),

Fig. 4.14(a)

g

_L vs. inductance

Fig. 4.14 (b)

L

²

g

_L²vs. inductance (nH) (Ω^-1)

(nH) (nHΩ^-1)²

respectively. The minimum of

L

²

g

_L² is searched in each bias current

I

_bias by decreasing the inductance (refer to Fig. 4.14(b)) and adjusting the cross-coupled pairs size to keep the same oscillation frequency. If

L

²

g

_L² is smaller than the minimum,

g

L is too larger (refer to Fig. 4.14(a)) to meet start-up condition. The start-up condition with a small-signal loop gain of at least

α

_min can be expressed as g_active ≥α_ming_tank where

g

_{tank ,}

g

_active are tank loss and effective negative conductance, respectively. The conductance

g

_tankis dominant by equivalent parallel conductance of spiral inductor

g

_L. Then a small-signal loop gain is selected to equal to 7. A symmetric active circuit with the same transconductance of cross-coupled pairs is used to get the better 1 f/ ³corner of phase noise [36].

There are two variables, bias voltage and tail current source size (W/L), to control the bias current

I

_bias . The MOS flicker noise is

W g WLC

g f K f

i _m

ox m n

2

2 2 2

∝

∆ = (4.22)

By varying the bias voltage and tail current source size (W/L) with keeping the bias current constant, the optimum situation with the lowest g_m² W is searched. PMOS is used for the tail current source because of low flicker noise.Therefore, the LC-tank components and bias current can be determined roughly from the minimum of

bias

L I

g

L^{2 2}/ .

Then, the size of cross-coupled pair can be fine tuned as follows by current source injection method. As indicated by [45.47], a small-signal sinusoidal current is injected at a proper frequency f into the output node and the signal is up-converted _m into two sidebands at f_o ± f_m due to the mixing mechanism in oscillation under large-signal operation as shown in Fig. 4.15. The larger the difference between sidebands and carrier is, the more symmetric the waveform is [45.46]. It implies the effect of nonlinear mixing is minimized. By varying the drain current and the size of cross-coupled pairs slightly with

g

_m keeping constant, the optimum situation with

Fig. 4.15 The spectrum with current injection atf _m

the lowest side band level is attained. The situation in terms of sideband to carrier ratio is shown in Fig. 4.16. The peak of the curve is the best choice.

Fig. 4.16 The optimum situation with the lowest side band level

Therefore, the procedure to design a low phase noise VCO is as follows:

A B

optimun

1. Choose the optimum width of the inductance to increase the Q factor.

2. Determine the LC-tank component and I_bias roughly.

3. Select a size of tail current source to keep the desired I_bias by minimizing its

flicker noise

W g C L W f

g K f

i _m

ox m n f

2 2

2 ∝

⋅

⋅

⋅

= ⋅

∆

4. The current injection method [45.46.47] on the output of the cross-coupled pairs to obtain the minimum up-conversion factor is used. By varying the drain current and the size of cross-coupled pairs slightly with gm keeping constant, the optimum situation of the operating point is located at the larger difference between the VGS-VT value and the sideband to carrier ratio.

在文檔中 金氧半導體元件雜訊對射頻積體電路的影響 (頁 73-77)