The performance of communication systems depends on the speed of
the devices used, and is typically specified by two figures-of-merit
(FOM). The first FOM is the transistor cut-off frequency f_{T};
the second FOM is the maximum oscillation frequency f_{max} (defined
as the frequency at which the current gain and the power gain become
unity, respectively).

To meet this challenge, the transistor geometric profile needs to
be scaled for higher f_{T} and f_{max}. Technology
scaling has driven this momentum to a high level of integration.1 Device
scaling has been the critical driving force behind high speed integrated
RF (radio frequency) and MW (microwave) solutions. Since the operating
frequency of the oscillator is limited by the f_{T} of the
transistors, RF and MW integrated circuits are often designed using
GaAs HBTs, which offer high f_{T}, but typically exhibit higher
flicker corner frequency (f_{c}) and are power hungry, and
are therefore not suitable for low phase noise and power efficiency
in signal generation applications.^{1–19} Si BJTs typically
have a low flicker corner frequency, but do not have sufficient gain
to sustain stable oscillation at RF and microwave frequencies because
of their limited f_{T} and f_{max}.^{14} SiGe
HBTs offer lower f_{c} and comparable f_{T} to GaAs
HBTs, making them the favorable choice for low phase noise and power-efficient
RF and MW signal generation applications.^{13,14} The oscillator
phase noise performance is one of the areas where SiGe HBT devices
outperform III-V devices.^{16,17} SiGe HBT has progressed over
the last decade from a digitally oriented technology to one well suited
for RF and microwave applications (due to its superior analog and RF
performance and its CMOS integration capability).^{13–19} Hence,
SiGe HBT technology is a promising contender among Si-based technology,
due to its advantages over CMOS technology such as higher f_{T},
lower noise and power-efficient performance. This article discusses
the impact of scaling on phase noise and the minimization of phase
noise in SiGe HBTs coupled voltage-controlled oscillators (VCO).

##### Scaling and noise performance characteristics

*Figure 1* shows the typical simplified common emitter equivalent
circuit broadband noise model of the SiGe HBT transistor.^{17} The
f_{T} and f_{max} of SiGe HBT can be given by

*where*

C_{be} = parasitic emitter base junction capacitance

C_{cb} = parasitic collector base junction capacitance

R_{b} = parasitic base resistance

g_{m} = device transconductance

τ_{b} = base transit time

τ_{e} = emitter delay time

τ_{bc} = base collector junction depletion layer time

All are technological scaling sensitive device parameters and can be optimized for higher fT and minimum noise figure for high frequency low noise oscillator applications.

Active devices (bipolar transistor) contribute their own set of problems
for the oscillator designer due to their inherent nonlinearities, noise
properties and temperature variations. The designer has limited control
over the noise sources in transistor, and only has a choice of device
selection, oscillator topology and operating bias point. For better
insight into the noise effects in the oscillator design, it is necessary
to understand how the noise arises in transistor and oscillator circuits.
Noise in the active device is characterized as a broadband noise (base
and collector current shot noise, and base resistance thermal noise)
and low frequency noise (1/f noise), which are sensitive to the scaling
of the active device^{3}

##### Broadband noise (thermal and shot noise)

The broadband noise in a bipolar transistor is due to the base current
shot noise 2qI_{B}, the collector current shot noise 2qI_{C},
the base resistance thermal noise 4kTR_{b} and the emitter
resistance thermal noise 4kTR_{e}. The mean square values of
the broadband noise generator (scaling sensitive parameters), as shown
in the figure for a frequency interval
Δf, can be described by

From Equations 1 to 4, the base and collector current shot noise can
be reduced by increasing the current gain b and cut-off frequency f_{T} for
a given profile of a SiGe HBT technology. Increasing the doping profile
of the base and reducing the emitter width can minimize the thermal
noise generated due to the base resistance.^{1} From Equations
1 to 6, maximizing the current gain β, the cutoff frequency f_{T},
and lowering the base resistance R_{B} in SiGe HBT, make the
technology promising for low phase noise signal sources (oscillator/VCOs).^{13–19}

**Low Frequency Noise (1/f Noise: Flicker Noise)**

The major contribution of low frequency noise is due to the flicker
noise (1/f noise), which lies in the base current of the SiGe HBTs.^{17} For
a spectral pure signal source, a lower 1/f noise is desired to minimize
the phase noise. However, the reduction of 1/f noise in semiconductor
technology is challenging, because it is sensitive to defects, particularly
in scaled technologies with low thermal cycles.^{1} The origins
of 1/f noise are varied, but in bipolar devices, traps associated with
contamination and crystal defects in the emitter-base depletion layer
cause 1/f noise. These traps capture and release carriers in a random
fashion and the time constants associated with the process give rise
to a scaling sensitive noise signal that describes a spectral density
of the form^{17}

*where*

Δf = narrow frequency bandwidth at frequency f

I_{B} = base current

K = constant for a particular device and technology

A_{e} = emitter area

a = flicker noise exponent (≅2 for SiGe HBTs)

b = flicker noise frequency shaping factor whose value is approximately unity

The mechanism for up-conversion of 1/f noise is caused by the nonlinear
nature of the circuits. The 1/f noise plays an important role in determining
the close-in carrier phase noise, which is unconverted to the carrier
frequency, resulting in a 1/f^{3} region near the carrier frequency.
The SiGe HBTs transistors exhibit typically a 3 to 4 times lower 1/f
noise, compared to Si devices.^{16}

**Oscillator Phase Noise and
Noise Factor F **

The oscillator phase noise can be given by^{3}

*where*

m = ratio of the loaded to unloaded Q

Q_{0} = unloaded Q

Q_{L} = loaded Q

f_{0} = oscillation frequency

f_{c} = flicker corner frequency

f_{m} = offset frequency from the carrier

F = noise factor

K_{0} = oscillator voltage gain

R = noise resistance of the tuning diode

k = Boltzman’s constant

T = temperature in degree K

From Equation 8, the minimum phase noise can be obtained by minimizing
the noise factor F for a given oscillator topology, operating frequency
and tuning range. The minimum noise factor F_{min}, for the
circuit shown, can be described by^{13–19}

*where*

From Equation 10, F_{min} at low frequency can be minimized
by increasing the value of the current gain β and reducing the
values of R_{B} at a given device bias (I_{C} = I_{DC1})
condition. However, F_{min} at low frequencies can be improved
by increasing β, but is limited by the negative impact on the
breakdown voltage BV_{CEO}. From Equation 11, at high frequencies,
F_{min} can be minimized by decreasing the value of R_{B} and
increasing f_{T} at a given device bias (I_{C} = I_{DC2}).
In SiGe HBTs, the parasitic emitter base junction capacitance C_{be} and
the parasitic base resistance R_{b} vary linearly with emitter
width w_{e}, allowing F_{min} at low and high frequency
regions to continue scaling down linearly with w_{e}. The parasitic
emitter base junction capacitance C_{be} and the parasitic
base resistance R_{b} decrease proportionally to the emitter
strip length L_{e}, whereas C_{be} and R_{b} increase
proportionally to the emitter width w_{e}. The noise factor
F is a technological scaling sensitive parameter and can be optimized
with respect to the transistor geometric profile of the scaled SiGe
HBTs to obtain the minimum noise figure for low phase noise oscillator
applications.

##### Scaled Device Multi-coupled Resonator VCO (2 to 6 GHz)

For high frequency applications, vertical scaling is done by reducing the base and collector transit times of the SiGe HBT technology, which requires a narrow and heavily doped base profile, with a higher Ge mole fraction.

Therefore, it results in a lower thermal budget, and an increase
in 1/f noise.^{1} *Figures 2* and *3* illustrate
the schematic and layout of the multi-coupled resonator-based VCO for
a 2 to 6 GHz frequency band (patent pending).

*Figure 4* shows the measured phase noise for scaling factors
1:1 and 1:2. As depicted, the device scaling increases the contribution
from 1/f noise (near the carrier), whereas it decreases the contribution
from base current shot noise and base resistance thermal noise (far
from the carrier).

As shown, the degradation at 1 kHz offset from the carrier frequency is 3 to 6 dB, whereas the improvement at a 1 MHz offset frequency is 6 to 12 dB.

Therefore, by analyzing the noise behaviors at near and far carrier
frequency offsets, due to the device scaling, the designer can improve
the noise performance by optimizing the conduction angle for a given
size of the device.^{2–5}

The VCO design approach based on scaling demonstrated in this work
enables power-efficient (5 V, 20 mA), extended frequency operation,
lower phase noise performance with a minimum 5 dBm power output over
the band (2 to 6 GHz), which is attractive for present and future generations
of wireless applications.^{5}

##### Coupled Mode Oscillators (N-push)

A high frequency oscillator signal can be generated, based on either
a scaled device (higher cut-off frequency f_{T}) operating
at a fundamental frequency or using a multiplier (frequency doubler).^{2–10} A
typical oscillator operating at the fundamental frequency suffers from
a low Q factor, insufficient device gain, lower device breakdown voltage
and higher phase noise at a high frequency of operation.^{3 }

The frequency doubler and other means of up-conversion may provide
a practical and quick solution to generate high frequency signal from
oscillators operating at a lower frequency, but it introduces distortions
and has poor phase noise performances.^{1–24}

This limitation has made it more attractive to pursue alternative
approaches such as N-Push VCOs, RF-MEMS (radio frequency micro electromechanical
system) VCOs, OEO (opto-electronic oscillator), YIG (yttrium-iron-garnet)
VCOs and others.^{18–21} Recently, an approach based
on a coupled oscillator principle in an N-Push (N = 2, 3, 4…k)
configuration has brought much attention because this principle allows
for an extended operating frequency range of active devices.^{7}

The coupled oscillator N-Push approach improves the phase noise performance by a factor of N (N is the number of the oscillators sub-circuits), and extends the operating frequency beyond the limitation caused by the cut-off frequency of available active devices.

*Figure 5* shows the system of N-coupled oscillators coupled
through the arbitrary coupling network as unilateral coupling, bilateral
coupling and global coupling.^{3} The coupled oscillators approach
discussed in this work minimizes the phase noise and extends the operating
frequency.^{5} The drawback of coupled oscillator (N-Push)
topology is the presence of higher order n^{th} harmonic components,
which may introduce significant 1/f noise up-conversion due to the
asymmetrical output waveform in the subsequent N oscillator sub-circuits
that forms the N-Push configuration. The expression for the oscillator
phase noise can be given by^{6}

##### where

From Equation 15, the 1/f noise up-conversion is closely related to
the symmetry property of the oscillator signal waveforms, and the 1/f
noise up-conversion can be reduced by minimizing the value of C_{0} and
by optimizing the slope and symmetry of the rise and fall time of the
oscillator output waveform.

The phase noise of the N-coupled oscillator in terms of a single uncoupled
oscillator can be described by^{8}

From Equation 16, the N-coupled oscillator system improves the phase
noise, compared to the single individual uncoupled oscillator, by a
factor N, where N is the number of the uncoupled oscillators in the
coupled N-Push topology.^{5–8}

##### Scaled Device Coupled Mode 4-Push Oscillators

*Figure 6* shows typical simplified N-coupled oscillators, coupled
through a common resonator and an example of a 4-Push oscillator. *Figure
7* shows the schematic of the 4-Push coupled oscillators operating
at a fixed frequency of 8 GHz (4f_{0}).

*Figure 8* depicts the simulated plot of the symmetrical and
asymmetrical output waveforms for the N-Push (N = 4) VCO, using scaled
SiGe HBTs (Infineon BFP620, scaling 1:2). For better insight about
the coupled mode N-Push domain, it is necessary to know how the noise
is affected by the scaling and symmetry of the waveforms.

From Equations 15 and 16, the noise performance and 1/f noise up-conversion can be optimized by improving the symmetry of the waveform in N-Push topology for a given size of the device.

*Figure 9* shows the improvement in phase noise performance
for a scaled coupled mode 4-Push VCO. At 1 kHz offset, it is of the
order of 6 to 10 dB, whereas at 1 MHz offset the improvement is of
the order of 8 to 15 dB for a device area scaling factor of 1:2.

*Figures 10* and *11* show the block diagram and layout
of the scaled device coupled mode multi-octave band 2-Push VCO (2 to
8 GHz).

The novel approach allows for a substantial reduction in phase noise
by dynamically minimizing the phase error and noise impedance transfer
function of the planar-coupled oscillators network over the operating
frequency band.^{7}

The typical measured phase noise is better than –90 dBc/Hz
at a 10 kHz offset from the carrier.^{3} Competing other alternative
semiconductor technologies may not deliver the same level performance
in terms of cost, size, power, linearity, tunability, adaptability,
reconfigurability and integrability for this class of VCOs using scaled
devices.

Fig. 10 Block diagram of a coupled mode 2-push, 2 to 8 GHz VCO (patented).

**Conclusion**

The multi-octave band design approach based on device scaling and optimum symmetry of the signal waveforms demonstrated in this work enables wide tuning, extended frequency of operation and lower phase noise performance, which are attractive for present industry applications.

This article describes the impact of device scaling on phase noise in coupled oscillators, which have recently emerged as strong contenders for radio frequency (RF) and mixed-signal applications.