**Fig. 1 Typical schematic of a dual-band
switched oscillator.**

Mobile phones and radios, operating in several modes, are typically switching between receiving and transmitting frequencies, and therefore require low phase noise signal sources (oscillators/VCOs) in each of the respective switched bands.

It is known that the oscillators exhibit trade-offs between power consumption and phase noise. To reduce the phase noise, power consumption and real estate area are increased.

To miniaturize the system and reduce the power consumption, multi-band, multi-mode system designers are forced to explore a frequency plan that employs one or more oscillators, phase-locked loop (PLL) frequency dividers, buffer amplifiers, filters, switching architectures and multipliers.

The miniaturization and the merging of multi-band systems impose stringent requirements on size, power, performance and configurability of the fully integrated transceiver systems.

The technology of the wireless devices also must allow for a smooth migration to future generations of communication standards with higher data rates.

Hence, the compact and power-efficient implementation of such multi-standard terminals calls for the need of an intelligent RF front-end that can achieve maximum hardware sharing for various standards.

Such a compact RF front-end would require reconfigurable multi-band VCO blocks rather than frequency multiplier or divider or switched resonator architectures.

Various techniques, such as switching between VCOs for separate bands,
using inter-modal multiple frequencies and switched resonators for
band selection have been proposed.^{1–25}

However, these methods result in circuits of large size, which are
current-hungry, narrowband and with poor phase noise performance. *Figure
1* shows the typical schematic of a dual-band (Band 1: 900 to 1800
MHz; Band 2: 1700 to 2600 MHz) switched voltage-controlled oscillator,
where the oscillators are alternatively switched with switches 1 and
2 to generate Bands 1 and 2.

Switched resonators (inductors or capacitor banks) suffer from the resistive and capacitive parasitics associated with the switches.

A recent paper^{2} shows a novel method of mode switching
(see *Figure 2*) in which both switches SW1 and SW2 are open when
any of the desired oscillation modes (mode 1: f_{1} = 2.398
GHz or mode 2: f_{2} = 4.733 GHz) are established.

This oscillator
uses a cross-coupled CMOS device with L1 = 2.34 nH, L_{2} =
0.86 nH, C_{1} = 1.6 pF and C_{2} =
0.96 pF. *Figure 3* demonstrates the concept of mode switching,
assuming that both switches SW1 and SW2 are normally open and the circuit
is oscillating at f_{1}.

In order to change the oscillation frequency to f_{2}, SW1
is closed for only a short duration, thereby reducing the region of
attraction for f_{1} and increasing it for f_{2}, causing
decay of the oscillations at f_{1} and growth of the oscillations
at f_{2}. Once the oscillations at f_{2} are stabilized,
SW1 can be opened again. The system keeps oscillating at f_{2} thereafter,
since it is one of its steady-state stable modes of oscillation.

As shown, SW1 is closed at t_{0} for 4 ns, enough for the
oscillation at f_{2} to stabilize. In order to switch from
f_{2} to f_{1}, SW2 is closed for a small duration.

It is understood that when the desired oscillation mode (mode 1 or
mode 2) is established, both switches are open. Therefore, the loss
and nonlinearity of the switches do not degrade the steady-state and
phase noise performance of the oscillator.

**Fig. 6 Frequency plan for a 2.4/5 GHz WLAN transceiver.**

This is fundamentally different from the traditional band-select oscillators,
where the dual-band resonances are obtained by alternatively switching
oscillators or switching inductors/capacitors (see *Figure 4*).^{10,20}

The main drawback of such architecture is that the band-selecting switch is placed in the signal path and thus deteriorates the performance of the oscillator because of its loss and nonlinearity.

In the case of the switched mode oscillator, the switching mechanism is limited to a short duration (between the stable modes of oscillations), just to get the desired band, as opposed to switching between two capacitors or inductors.

However, the present solutions to the dual-band systems are not concurrent in a real sense, because the oscillators are alternatively switched between different resonators for generating the required different frequencies and the design technique does not allow the signals to be generated at the same time.

Therefore, they suffer from power consumption, larger area and design cycle time.

In this work, a novel technique is proposed, based on a dynamically
controlled multi-mode oscillation technique using asymmetrical planar-coupled
resonator networks to extend the tuning range of the oscillators.^{17,24}

The proposed topology discussed in this article uses a new class of
oscillator that generates multiple synchronous frequencies by using
higher order (> 2), multi-coupled planar resonators (MCPR), which
offers concurrent solutions by synchronously generating multiple frequencies
for different bands without using a multiplier or switching resonators/oscillators
network, therefore resulting in a reduction in power consumption, area
and design cycle time.^{23–25}

#### Theory

The next generation of wireless communication systems is supposed to be frequency agile and must be able to seamlessly span multiple frequency bands dynamically to cover different global standards.

Rapid evolution in the field of wireless communication and the convergence of multiple communication protocols has led to the integration of multiple complex functionalities in wireless portable devices.

Convergence of various standards, such as WLAN, into a motherboard of a computer or into a cell phone (3G and 4G) has led to added functionality in each system. The most commonly used frequency bands are the 2.4 to 2.5 GHz ISM band and several frequency bands from 5.15 and 5.85 GHz, with several communication standards defined in the IEEE 802.11 standards.

In order to give the user more freedom, phones that are able to cover more than one of these bands require reconfigurable concurrent signal sources for multi-band, multi-mode wireless communication systems.

*Figure 5* shows the typical schematic block diagram of a dual-band
(2.4/5.0 GHz) transceiver system, where a single signal source (oscillator)
with two or more frequency bands is the first step towards a fully
integrated multi-band design.^{1} *Figure 6* illustrates
the divider and the switching-based architecture of the frequency plan
for a 2.4/5.0 GHz WLAN transceiver system.^{8} As shown, the
approach uses a single VCO at 8 GHz with a divider 1 (+ by 2) in a
frequency synthesizer to generate a 4 GHz signal, which is followed
by a divider 2 (+ by 4).

The output of divider 1 (4 GHz) and divider 2 (1 GHz) signals are mixed in a QUAD SSB mixer to generate the 5 GHz signal, which is further divided to obtain the required 2.4 GHz signal. The implementation utilizes multiple buffers, filters and divider networks.

Frequency multipliers can be an alternate option, but they are seldom
used for the final stage of frequency conversion because of the difficulty
in obtaining differential outputs at higher frequencies, which are
required by quadrature converters.^{9,10} The basic principle
of a multi-mode radio is to process two or more signals of differing
frequencies at the same time, but using only one processing Tx-Rx chain.^{6,7}

The n^{th}-order (n > 2) MCPR-based, multi-mode RCO demonstrated
in this work can satisfy the present demand for low cost, dual-band,
low noise, power efficient, wide tuning range and compact size, and
is easily amenable for integration in chip form.

#### Single Frequency Tunable Wideband Oscillator

Typical single frequency tunable oscillators use a grounded base or grounded emitter circuit for generating a negative resistance at one port, which is usually terminated with a parallel or series LC-resonant tuned circuit.

For wideband tunability, the required negative resistance over the band is generated by the feedback base-inductance (in the grounded base topology), but the polarity of the reactance may change over the frequency band and can lead to the disappearance of the negative resistance as the operating frequency exceeds its self-resonance frequency (SRF).

There are two primary constraints, which limit the oscillator circuit topologies: the first is the transistor and its package; the second is the large capacitance change required to tune the oscillator over an octave band.

The common emitter (CE) and common base (CB) are the common topology
for a wideband VCO’s design. *Figure 7 *shows the CE topology,
which uses a capacitive feedback network with C_{1} and C_{2} to
create the negative resistance looking into the base of the transistor.^{3}

*Figure 8* shows the common base (CB) topology, which uses an
inductor L_{b} in the base of the transistor to generate the
negative resistance R_{n}(t) looking into the emitter of the
transistor.^{4,17} As shown in the CE topology, small values
of the feedback capacitances C_{1} and C_{2 }generate
a large negative resistance and allows for a wide tuning range at the
cost of heavily loading of the resonator and wide conduction angle,
hence poor phase noise performance.

For optimum phase noise performance, the active device is driven at a large-signal drive level that corresponds to a narrow conduction angle, and this restricts the lower limit of the feedback capacitors.

The drive level is directly proportional to the feedback capacitor
C_{2}^{3}; therefore, this topology is best suited
for narrow tuning range (10 to 30 percent) VCOs because large values
of feedback capacitors C_{1} and C_{2} will raise the
loaded Q of the resonator at the expense of lesser tuning ranges and
lower negative resistance.

The effective loading of the resonator for the common base (CB) oscillator
configuration is due to the series combination of the load resistance
and the transconductance of the transistor (the influences of g_{ce},
g_{be} and C_{be} are neglected for simplification).

In this case, the loaded Q of the resonator is unaffected by the negative
resistance generated by the feedback inductance L_{b} of the
three-terminal device (bipolar/FET) and this configuration is therefore
best suited for a wideband (octave-band) VCO application. *Figures
9* and *10* show the general series feedback topology, and
small-signal equivalent circuit for the purpose of the resonance frequency
and noise analyses.

The steady-state oscillation condition for series feedback CB configuration is given by

where

R_{osc}(I_{L},ω) = negative resistance components
generated by the three-terminal active device (bipolar)

I_{L} = load current amplitude

ω = resonance frequency

Z_{osc} = current and frequency dependent output impedance

Z_{L} = only function of frequency

From Equations 1 and 2

where Z_{11}, Z_{12}, Z_{21}, Z_{22} are
the [Z] parameters of the transistor. From Equation 4, Z_{osc},
R_{osc}, X_{osc} and R_{n} can be given by

where

R_{n} = negative resistance of the series feedback oscillator

g_{m}(t) = large-signal transconductance

The total noise voltage power within a 1 Hz bandwidth is^{3}

The first term of Equation 9 is related to the thermal noise, due to the loss resistance of the resonator tank, and the second term is related to the shot noise and flicker noise in the transistor.

From Equation 9, the phase noise can be described by^{3}

where

(ω) = ratio of sideband power in a 1 Hz BW

ω = offset frequency from the carrier

ω_{0} = resonance frequency

Q_{L} = loaded Q of the tuned circuit

K_{f} = flicker noise coefficient

AF = flicker noise exponent

kT = 4.1x10^{–21} at 300K

R = equivalent loss resistance of the resonator circuit

I_{c} = collector current

I_{b} = base current

V_{cc} = collector voltage

The performance of an oscillator can be evaluated by the figure-of-merit (FOM), and can be described by

The first and third terms of Equation 11 represent the contributions
of phase noise and power consumption (P_{DC}) to FOM, respectively.
From Equation 11, the phase noise for a given offset has greater impact
on FOM than the power consumption does for a given oscillator frequency
f_{0} (ω_{0} = 2πf_{0}).

#### Multi-frequency (Multi-band and Multi-mode) Oscillator

Conventional oscillators are governed by second-order nonlinear differential
equations and can only generate periodic waveforms, a single frequency
and its harmonics. Oscillators with higher order nonlinear differential
equations have multiple modes of oscillations and can generate multiple
independent frequencies, individually or simultaneously.^{14–16}

he paucity of literature on multi-ban, multi-mode oscillators, together with a lack of experimental verification of the underlying theories towards achieving the desired mode of oscillations in a controllable way, has been a strong motivator for research work.

The phase noise of higher order mode oscillators has not been investigated
previously either.^{2} A single frequency tunable wideband
oscillator utilizes a varactor-tuned, second-order resonator network
(parallel LC or series LC network) to generate the desired frequency
signal.

The impedance response of the parallel LC and series LC resonator networks exhibit an anti-resonance (high parallel resistance: ideally infinite) and resonance (low series resistance: ideally zero resistance), respectively.

For simultaneous multi-frequency resonance, the order of the resonator network requires it to be increased, depending upon the number of frequency signals for the respective bands.

The main problems in this design are generating simultaneously a
negative resistance over the multiple separate distinct bands. *Figure
11* shows the typical simplified schematic of a multi-frequency
(multi-band and multi-mode) oscillator of nth-order that can be explained
with the help of the single band negative resistance approach.

From Equations 1 and 2, the steady-state oscillation condition for
multi-band (n^{th}-order) can be explained and described by

where R_{osc}(I_{L}, ω_{1}, ω_{2}, ω_{3}…ω_{n})
is the negative resistance components generated by the three-terminal
active device (bipolar), IL is the load current amplitude, ω_{1}, ω_{2}, ω_{3}…ω_{n} are
n distinct resonance frequencies, Z_{osc} is the current and
frequency dependent output impedance and Z_{L} is only the
function of frequency.

#### Dual-band, Dual-mode Oscillator

The idea of negative resistance in a single band oscillator was extended
to a dual-band oscillator by Schaffner,^{15,19} where the oscillator
has to simultaneously satisfy the resonance conditions for two distinct
frequencies f_{1} and f_{2}, respectively. Schaffner^{15 }investigated
mathematically the possibility of simultaneous oscillations at two
independent and dependent frequencies based on a nonlinear negative
resistance active device connected across a higher order (n = 4) parallel
LC resonator network. Schaffner investigated both synchronous (f_{2}/f_{1} =
p/q = integer (⇒ rational number) and asynchronous (f_{2}/f_{1} =
p/q ≠ integer (irrational number) simultaneous oscillations in
oscillators using differential equations.

The method is a general method for determining sufficient conditions
for the existence and stability of periodic solutions of a class of
nonlinear vector differential equations. For transient analysis, the
fourth-order system is broken into two second-order systems and the
superposition theorem is applied to obtain the desired solution for
dual-mode signal generations at frequencies f_{1} and f_{2}.
The independence of the frequencies is related to the irrational ratio
of the frequencies (f_{2}/f_{1} ≠ integer), whereas
a rational ratio between the two frequencies (f_{1} and f_{2})
implies that the signals are dependent on each other through their
phase. *Figure 12* shows the typical schematic of a dual frequency
oscillator that uses a higher order of resonator network (fourth-order
instead of second-order, LC resonant circuit, for a single frequency
oscillator). From Equations 12 and 13, the oscillator circuit has to
satisfy the necessary condition for guaranteed stable oscillations
for two frequencies (f_{1} and f_{2}). At a given frequency,
the impedance with a negative real part is observed at the emitter
terminal by adding an inductor of suitable value at the base terminal.
The design philosophy for single frequency oscillation can be extended
to apply to dual frequency oscillations. The fundamental criterion
is to support simultaneously negative resistance at two distinct frequencies
by synthesizing two inductors of different values. For stable oscillations,
the resonator network at the base of the transistor terminal should
be designed to provide different values of inductance (two degrees
of freedom) at the desired center frequencies. Intuitively, a higher
inductance value will be needed at f_{2} and a relatively lower
inductance value is required at f_{1} (f_{2} > f_{1}).
Since a simple parallel LC network is insufficient to provide such
a behavior, a fourth-order resonator is synthesized using L_{1}–C_{1} and
L_{2}–C_{2}. In general, a parallel-connected
LC resonator will be inductive before the tank resonance (anti-resonance)
and capacitive after the resonant frequency. At a given frequency the
effective inductance (L_{eff}) can be determined from a parallel-connected
resonator by performing network analysis to calculate the Z_{in} of
a resonator. *Figure 13* shows the simulated phase noise plot
of the dual frequency (2.5/5.0 GHz) oscillator.

#### Validation

An oscillator with a high order (> 2) resonator has multiple stable
modes of oscillations. By using a proper nonlinear active topology
and resonator component values, the higher order oscillator (> 2)
can generate more than one resonant frequency. For example, a fourth-order
oscillator can generate either of the two distinct frequencies ω1
or
ω2. *Figures 14*, *15* and *16* show the fourth-order oscillator
that can generate either of the two distinct frequencies ω_{1} or ω_{2} or
both ω_{1} and ω_{2}. For validation purposes, the
prototype is designed to generate two synchronous bands (fourth-order resonators)
by incorporating two second-order parallel resonators in the base of the bipolar
transistor.

*Figures 17* and *18* show the schematic and layout of the
reconfigurable dual frequency tunable concurrent oscillator^{18,25} that
uses a fourth-order resonator network to satisfy the necessary conditions
for guaranteed and stable oscillation conditions for two different
frequencies (ω_{1}, ω_{2}) that can be tuned
for two different frequency modes (bands) such as 2.45 to 2.65 GHz
and 4.85 to 5.25 GHz. As a result, a simultaneous reduction in power
consumption, area and design cycle time can be achieved using a concurrent
solution.

The prototype is designed to generate two synchronous bands (fourth-order
resonators) by incorporating two second-order parallel resonators in
the base of the bipolar transistor. From Equations 12 and 13, the equivalent
impedance at the emitter terminal must support a negative real part
at two distinct frequencies (ω_{1}, ω_{2}).
This can be achieved by synthesizing two inductors of different values
at the base of the transistor corresponding to (ω_{1}, ω_{2})
for simultaneous sustained oscillation conditions. The resonator network
at the base of the transistor (Q_{1}) was designed in a MCPR
medium to provide different values of inductance (two degrees of freedom)
at the desired center frequencies.^{2–7} In general,
a parallel LC resonator will be inductive before the tank resonance
(anti-resonance) and capacitive after the resonant frequency. At a
given frequency the effective inductance can be calculated from a parallel-connected
resonator by performing network analysis to calculate the Z_{in} of
an equivalent resonator network. Since the active device (Q_{1})
is sensitive to perturbations at all three nodes (base, emitter and
collector) of the BJT, either of them can be tuned to obtain wideband
tunability for different bands of oscillations for given values of
R_{M1} and R_{M2} at P_{1} and P_{2}.
Intuitively, a higher inductance value is needed for Mode 1 (2.45 to
2.65 GHz), and a relatively lower value of inductance is required at
Mode 2 (4.85 to 5.25 GHz). For wideband tunability, the effective values
of inductance for different modes of oscillation are synthesized by
incorporating a tuning capacitor across the resonators network at the
base of the transistor Q in such a way that they provide the required
negative resistance and reactance (inductive or capacitive) at the
emitter terminal of the transistor Q over the required operating bands.^{25} *Figure
19* shows the measured phase noise plot of the reconfigurable concurrent
dual-band oscillators. The measured phase noise performance for Band
1 (2.45 to 2.65 GHz) and Band 2 (4.85 to 5.2 5 GHz) are typically better
than –120 dBc/Hz at 1 MHz offset from the respective carrier
frequencies. The circuit operates at 5 V, 20 mA and gives a typical
output power of 3 dBm over the bands. The phase noise of the fourth-order
oscillator, when generating only one of its resonant frequencies, is
comparable to the phase noise of a second-order oscillator using the
same active topology and resonator quality factor. Furthermore, the
fourth-order oscillator has a better phase noise and/or a higher tuning
range in VCO implementations, compared to the commonly used switched
resonator oscillators.^{2} When the system begins to oscillate
in dual-mode (Modes 1 and 2), a mode leakage occurs, and therefore
how much mode leakage is allowed depends on the spectral selectivity
of the succeeding filter and the system requirement.

#### Conclusion

The state-of-the-art, dual-band, multi-mode RCO reported in this article
can be further extended to other higher stable mode such as triple-,
quadruple- and n^{th}-order modes. Hence, it can replace traditional
multiple oscillators and the technology is compatible with existing
IC process.