Chapter 2 Section II
II. 2.2 Flicker noise in mixers
CMOS transistors suffer from high flicker noise which is inversely proportional to the device area [4]. This is produced from CMOS process and unable avoided. So the size of CMOS transistor is influenced in flicker noise.
Double balanced mixer in DCRs comprises transconductance stage, switch stage with local oscillator, and IF loaded stage. Because flicker noise in RF stage is low frequency noise, it will be up-converted to vicinity of LO frequency. And it will not contribute any flicker noise in DCR systems. Load stage is used of polysilicon resistors which are free of flicker noise. Mismatches in the switch pairs will also
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generate a small amount of flicker noise at the output. Therefore, switch stage is significant contributed flicker noise at baseband [5].
Flicker noise in DCRs is determined in switch pair devices. There are two different mechanisms that generate flicker noise. The first one is direct mechanism, which is generated in the switching transitions. When LO stage commutating motion, it will generate noise pulse trains. Because noise transfer function is linear from each device, the superposition theory holds. The low frequency in switching pairs should be calculated as the voltage source Vn(t). Fig. 2.23 shows the noise pulses resulting in flicker noise at mixer output [6]. Because mixer needs sine wave of local oscillator to drive switching quad, the large sine-wave LO signal accompanies noise. The noise advances or retards the time of zero crossing by ∆t=Vn(t)/S. So the noise pulse trains of random widths ∆t and amplitude of 2I at a frequency of 2ωLO represent at the output.
Fig. 2.23 Noise pulses resulting in flicker noise at mixer output [6]
( )
V tn
t S
∆ = (7)
Over one period, the average of output current is [5]
,
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where I is the bias current of RF transconductance stage, T is the LO period, Vn is the flicker noise of switch pairs, and S is the slope of the LO signal. Weff and Leff are the effective width and length, Cox is the oxide capacitance, f is frequency, and Kf is a process parameter [5]. In the indirect mechanism, capacitance Cp is main determined flicker noise. It can describe as following equation
( )
where Cp is the tail capacitance between LO switch stage and RF transconductance stage with all parasitic capacitance. T is the LO period, gms is the transconductance of LO switches, ωLO is the frequency of local oscillator, and Vn is equivalent flicker noise of LO switches [5].
So, there are some topologies to reduce flicker noise from above equation. From (8), increasing the slope of the LO signal and reducing the equivalent flicker noise of switching transistors can alleviate the influence. It needs to increase sizes of the switch transistors. However, it has some drawbacks. The large sizes of switching transistors increase the parasitic capacitance at common source of switch stage and increase the flicker noise indirectly.
Reduction of bias current of the switch stage can lower the noise pulses and improve flicker noise. Conventional Gilbert cell with current bleeding is proposed in Fig. 2.24. However, this technique has some important drawbacks. When reducing the biasing current of the switch pairs, the impendence as seen from RF transconductance stage into switch stage (1/gms) will be increased. It allows more RF leakage current flowing into the bleeding circuit. The leakage current will also be shunt by the parasitic capacitance at the node between RF stage and switch stage.
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This decreases the gain and reduces the mixer linearity. The dynamic current bleeding circuit is proposed to solve the problems [6]. Fig. 2.25 is presented the conventional Gilbert cell mixer with dynamic current bleeding.
Fig. 2.24 Conventional Gilbert cell with current bleeding
Fig. 2.25 Conventional Gilbert cell with dynamic current bleeding
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Since the noise pulse trains is only present at the switching instant of LO switch quads. A dynamic current bleeding is injected to the core through a switch control circuit at the switching instant of switch pairs. Fig. 2.26 shows the theory and idea for dynamic current bleeding [6]. The switching event controls by the nodes at common source of switch pairs (Fig. 2.26 nodes A and B). The waveform of nodes A and B is shown in Fig. 2.26 (b). Because the LO provides large signal, the voltage waveforms at nodes A and B are just like full wave rectifiers. The injection of dynamic current ID
occurs when voltage is small. This way reduces the height of noise pulse directly, and noise pulse at the output is close to zero as shown in Fig. 2.26 (b). On the other time, the switch is close and generates no current to circuit.
Fig. 2.26 (a) Dynamic current injection (b) Nodes waveform [6]
There are a few drawbacks in this topology. It needs high power of LO to drive switch stage and its conversion gain is low. It is just like a passive mixer. In spite of the imperfect of switching, this technique is still improved significant.
To improve flicker noise in the mixer, reducing the bias current of the switch
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stage and tuning out the tail capacitance from (8) and (10). Current bleeding technique is decreased the bias current of the switch stage, and has a few drawbacks described above. Fig. 2.27 shows the conventional Gilbert cell mixer with current bleeding and one resonating inductor. Even though the current bleeding can reduce to LO bias current to improve flicker noise, it is generated the flicker noise from tail capacitance in indirectly mechanism. In order to diminish the tail capacitance, the choice of small size device in RF and LO stage is an idea. Nevertheless, CMOS transistors suffer from high flicker noise which is inversely proportional to the device area [4]. So the other way is using one inductor to tune out the tail capacitance instead of changing the size of MOS. The inductor is connected from one path at the nodes between RF and LO stage to the other path as shown in Fig. 2.27. The equivalent model of double-balanced mixer with current bleeding circuit and one resonating inductor is shown in Fig. 2.28 [7].
Fig. 2.27 Current bleeding technique with inductor
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Fig. 2.28 Equivalent model of double-balanced mixer with current bleeding circuit and one resonating inductor [7]
The gm1 is the transconductance of the switch transistor M1, and gm2, gm3, gm4 are the same as gm1. Cp is the parasitic capacitance at the node of transconductance stage and switch stage. RB is the load of the transistor as current bleeding. Lp is the resonating inductor. As shown in Fig. 2.28, the resonating inductor tunes out the tail capacitance and protects RF signal current from flowing into shunt path. This technique improves conversion gain and flicker noise simultaneously. So this technique is adopted in our design. The significant improvement is presented.
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