A Tail Current-Shaping Technique to Reduce Phase Noise in LC VCOs 指導教授 : 林志明 教授 學 生 : 劉彥均 IEEE 2005CUSTOM INTEGRATED CIRCUITS CONFERENCE Babak Soltanian and Peter Kinget Department of Electrical Engineering Columbia University New York, NY 10027

Outline Introduction Tail Current Shaping Measurement Result Conclusion

Introduction The main contributors to the phase noise of a cross- coupled MOS VCO are (1) The cross-coupled switching transistors (2)The tail current source (3) AM-to-FM noise conversion by the varactors (4) Thermal noise associated with the loss in LC resonator

The inductor’s thermal noise contribution is reduced by implementing higher Q inductors. The AM-to-FM noise conversion of the varactors can be lowered by discrete tuning and reducing the VCO’s gain, e.g., through employing a switched capacitor array [1]. Different filtering techniques have been proposed to reduce the contribution of the tail current source to the phase noise [2] [3].

For long channel MOS transistors, the power spectral density of the current noise of the switching MOS devices in saturation is directly proportional to the square root of the current they carry. The phase noise generated by the switching devices can be influenced by manipulating their current waveform.

The phase variations in the VCO output in response to a noise current injected into the tank is a periodic function, often referred to as the impulse sensitivity function (ISF) [4] It is maximum when the output voltage is at the zero- crossing instants and it is minimum when the output voltage is at its maximum or minimum value.

(a) Impulse injected at the peak, (b) impulse injected at the zero crossing,

The VCO’s phase noise can thus be reduced if the current is injected into the tank at the right moment, i.e., when the ISF is minimum. This paper present a circuit technique to reduce the phase noise in differential CMOS LC-VCOs by shaping the tail current.

Tail Current Shaping

In steady-state θ is its phase delay compared to the output voltage

When M1 is on and M2 is off, the circuit is similar to a source follower [5], Assuming that the output resistance of the tail current source is much larger than the impedance of at

is obtained from the following equation: For a typical circuit, the phase delay is approximately: and the amplitude is

Given this,the current through,, is now. The tail current injected into VCO2,, is where is the DC current through M3. Through appropriate circuit sizing we can set the amplitude of equal to the DC current so that ( ), we obtain

is a sinusoidal waveform with a peak-to-peak amplitude of 2. If we size the devices so that θ is set to approximately π/4, the tail current peaks align with the peaks of the output voltage.

M1 or M2 then inject the tail current into the tank at the instants where the oscillator’s output phase is less sensitive to injected noise currents. At the zero-crossings of the VCO output, where the VCO’s phase sensitivity to noise currents is maximum, the tail current becomes zero and M1 and M2 do not carry any current and generate no noise. As a result, the phase noise of VCO2 is expected to be smaller than of VCO1.

A. DC to RF Conversion The differential output amplitude (2A1) for VCO1 is: The differential output amplitude (2A2) for VCO2 is: VCO2 is expected to have a 33% larger amplitude than VCO1 for the same DC bias current and thus a better DC to RF conversion efficiency thanks to the tail current shaping.

B. Phase noise The phase noise of VCO1 and VCO2 in dBc/Hz at an offset frequency of can be accurately estimated using the following formula after [4]:

The tail current shaping technique improves the phase noise through three different mechanisms. (1) DC to RF conversion (2) Narrower drain current pulse(Fig. 4, Fig 5) (3) is a noise filter for tail current source

Measurement Result

Process0.25μm BiCMOS Frequency1.755GHz~ 2.123GHz Power dissipation2.25mW Phase -120dBc/Hz FOM185.5 Supply Voltage1.5V

Figure of merit (FoM) [6]:

Conclusion The measurement results are compared with a reference standard VCO; the tail current shaping technique improves the phase noise by more than 3 dB at the 600 kHz offset frequency, for 1.75 GHz and 2.12 GHz output carriers. The presented technique does not require extra power dissipation and consumes only a small silicon area. The presented circuit techniques can be applied for other VCOs as well.