ISF - Impulse Sensitivity Function

The VCO can be examined using the ISF, Impulse Sensitivity Function. The ISF is a measure of the phase noise caused by a small signal pulse injected to the circuit.
A convulotion of the ISF with the noise function will result the circuit phase noise.

VCO Pulling

The VCO has sensitivity to load changes. This sensitivity can be defined by:

Kload=dFosc/{delta}Cload

VCO pulling occurs due to dynamic operations of transmit and receive paths.

VCO's FOM

A Figure Of Merit is a quantity used to characterize the performance of a VCO relative to other VCOs' of the same type.
The power, phase noise, frequency of oscillation, offset from carrier trade offs all are taken in the FOM value:




.
w0 is the oscillation frequency
dw is the frequency
dw is the offset from the carrier
L(dw) is the phase noise at the specified offset
Pdiss is the DC power consumed by the VCO core.


FOMT also factors in the tuning range.
FOMT is given by:


.

where FTR is the frequency tuning range of the VCO.
See a spread sheet of the FOM calculation

Oscillator Voltage Amplitude

For LC VCO's there are a few factors that limit the output voltage amplitude:
- The supply voltage
- The bias current
- The frequncy of oscillations
- The inductance of the inductor
- The tank resistance


If we increase the bias current of the VCO the amplitude will increase in direct proportion until the voltage will reach Vlimit.

Vout = Ibias * Rtank

This regime is called the Current Limited Regime.
Now if we keep increasing the bias current the VCO, the output swing will keep Vlimit (with a small change).

Vout = Vlimit

This regime is called the Voltage Limited Regime.

Bands Tuning Range Calculation

The VCO frequncy is changing continuously with the input voltage.
In order to increase the VCO frequency tuning range without a significant phase noise degradation, we use sub-bands.
The implementation is usually a digital controled bank of switched capacitors.
The digitally conrolled bands should have enough overlap to support all Process Voltage and Temperature (PVT) variations.
The tuning range should support all PVT.
Some definitions:
OL - Over Lap between two bands
TR - Frequency Tuning Range of a single band
Gap - The frequency distance of two bands



Bands Over Lap [%] = OL/TR *100

Bands Gap [%] = Gap/TR *100


The switch design
The switch should have low enough resistance so it will not degrade the quality facator Q of the tank.
This implies a large W/L ratio. on the hather hand increasing W will increase the capacitance of the switch at "Off" state.
Here you have one of the important tradeoffs in the VCO design: Q of the switch at "On" vs. C of the switch at "Off".

SSA Phase Noise Measurement

The Phase Noise measurement with Spectrum Analyser can be done only if the Spectrum Analyser noise floor is lower then the DUT.
The SSA employs a cross-correlation technique to enhance the phase noise sensitivity without employing a clean reference source.
This technique essentially cancels the system noise.
The SSA consists of two independent signal paths with built-in reference sources, as well as local oscillators for signal downconversion that creates signals that are uncorrelated with each other. When the two signals are correlated and vector summed, the vector (amplitude and phase) of the two signals is emphasized. However, if two signals are uncorrelated, their vector sum is canceled, so the internal noise from references such as sources, ADCs and mixers can be canceled. The amount of noise cancellation depends on the “number” of correlation and is based on root N (the number of correlation). Correlation of 10 times produces a 5 dB noise floor improvement, and 100 times correlation produces a 10 dB improvement.

Standard measurement range for the newest analyzer is 10 MHz to 7 GHz, but it can be increased to 110 GHz with currently available downconverters.
The signal source analyzer provides a one-step phase noise measurement by eliminating time-consuming procedures.

Phase Noise Measurement

Phase Noise is a basic property in VCO design. Measuring Phase Noise requires a carefull treatment.
One way of is to measure phase noise directly on a spectrum analyzer. This measurement can be done as long as the analyzer has better phase noise than the measured source.
VCO phase noise can be measure when the VCO is locked in the PLL loop or in open loop.
The first method is easier to measure but then you see phase noise of both VCO and the loop.
The second method gives directly the VCO noise, but you have to hold Vtune with a very clean source.

EVM Calculation

The error vector magnitude represents theEuclidian distance between the ideal symbolcoordinate and the actual recorded symbol.
EVM is a way to measure and quantify the performance of a comunication system. A comlex signal sent by an ideal transmitter or received by a receiver would have all constellation points precisely at the ideal locations, however various imperfections in the implementation (such as carrier leakage, low image rejection ratio, phase noise etc.) cause the actual constellation points to deviate from the ideal locations. Informally, EVM is a measure of how far the points are from the ideal locations.

EVM calculation:
EVM ≈ 100%*Sphi(f)*π/180 ........Error vector magnitude due to phase noise.

Jitter calculation

Jitter is the time domain represantation of the frequency fluctuations.
Jitter due to phase noise:

Jitter = Sphi(f)/(foscx360\deg)

where Sphi(f) is the Spectral density of phase modulation, also kown as RMS phase error [degrees]:

Jitter can be defined to variations of the signal amplitude, frequncy, or phase. It can be measured in terms of RMS, peak to peak etc.

Integrated Phase Noise

Integrated Phase Noise is a method of expressing the quality of the signal source. The IPN is calculated from the phase noise measurement.
Integrated results may be displayed in a number of formats:

Integrated single sideband phase noise [dBc]:

\int{L(f)}}df

---------------------------------------------------------
Spectral density of phase modulation, also kown as RMS phase error [degrees]:

Sphi(f) =(180/\pi)\sqrt(2\int{L(f)}df)\)  

---------------------------------------------------------
Spectral density of frequency fluctuations, also known as RMS frequency error or residual FM [Hz]:

Snu(f) =\sqrt(2\int{L(f)f^{2}}df)

---------------------------------------------------------

Oscillator Phase Noise

Phase Noise is a frequncy represantation of random fluctuations of the phase of the oscillator output signal.
Phase noise is perhaps the most important parameter in many oscillators.
Ideally, the spectrum of an oscillator is an impulse at a single frequency. However,
in any practical oscillator, the spectrum has power distributed around the desired oscillation
frequency, in addition to power located at harmonic frequencies. This undesirable power distribution around the desired oscillation frequency is known as phase noise.

LC VCO

LC oscillators are probably the most common type of oscillators used in RFIC design. LC oscillator is part of the familly of the resonant oscillators and can be designed for a fixed frequency and variable frequency operation (with the use of a varactor).
LC VCO consist of two main stages: gain stage and LC tank.

LC VCO advantages:
Outstanding phase noise and jitter performance at high frequency.

LC VCO disadvantages:
1) Contains an inductor which is large area component and thus is less suitable for VLSI design
2) High power consumption
3) Relatavly small tuning range.

What Is VCO

VCO or Voltage Controlled Oscillator is an electronic citcuit that it's output frequncy is controlled by the input control voltage.
The most common types of VCO's are LC VCO and ring oscillator.

Quality Factor

Quality factor or Q , is a measure of the quality of a resonance circuit. The higher the Q value, the narrower the bandwidth of the resonance.
A higher Q indicates also a lower rate of energy dissipation relative to the oscillation frequency

Q = \omega \times \frac{\mbox{Energy Stored}}{\mbox{Power Loss}}

Q for parallel RLC circuit:

Q = \frac {R} {\sqrt\frac{L}{C}}

Q for serial RLC circuit:

Q = \frac{1}{R} \sqrt{\frac{L}{C}}

For complex impedance:

Q = \left  \frac{X}{R} \right 

Impedance

XL=2*pi*f*L
XC=1/(2*pi*f*c)

Q = R/wL