Advances in Circuits, Systems, Signal Processing and Telecommunications
Design of Wideband Distributed VCOs
F. CANNONE, G. AVITABILE, G. COVIELLO
Dipartimento di Ingegneria Elettrica e dell’Informazione
Politecnico di Bari
Via Orabona 4 – 70125 Bari
ITALY
f.cannone@poliba.it http:// etlclab.poliba.it
Abstract: - The paper describes a multi-band Distributed VCO topology suitable for multi-standard
transceivers. This topology gives an optimum trade off among the multi-band capability and phase noise
requirements. After a brief presentation of the DVCO operations a detailed analysis of the oscillation conditions
for the topology is presented leading to general expressions for the amplitude and frequency of oscillation. A
prototype with a measured 21.2% tuning range validates the theory.
Key-Words: - Switched circuits, Microwave circuits, Voltage-controlled oscillators
travelling wave VCOs and standing-wave VCOs
[12].
Theoretically, the DVCO could benefit of the
wide bandwidth of the amplifier and it allows to
design fully integrated VCOs which operate at
higher frequencies compared with the integrated
LC-VCOs for a given technology. The literature
proposes several examples of DVCOs operating in
the forward gain mode [4]-[11], but none of these
solutions exploits completely the potentiality of
such class of oscillators in terms of wide tuning
range.
The key feature that offers the DA is the
possibility to take advantage of its wide band to
design a multi-band VCO operating on different
bands for different wireless standards. The
topologies proposed in [13] is a solutions striving to
this purpose. The approach proposed in [13]
separates the amplification from the phase shifting.
In this way, the DA can play the role of a “loop-gain
tank”. Thus, the amplifier can potentially sustain the
oscillations over a very wide bandwidth and jointly
provide uniform performances in terms of phase
noise, output power and harmonics suppression. The
way in which the phase shift is implemented is
critical to correctly achieve the scope.
Section 2 reports a detailed analysis of the
oscillation condition for the topology presented in
[13], leading to general expressions for the
amplitude and frequency of oscillation while in
section 3 the tuning technique is described. Using
these equations a DVCO has been designed, and the
measurements results are reported in section 4.
1 Introduction
Modern telecommunication units commonly
integrate different standards with their everincreasing bandwidth associated to each of them.
This circumstance relates to the concurrent need for
mobility and fast data rates of the customers.
Consequently, frequency sources with multi-band
characteristics, joint to low-power consumption and
stringent phase noise performances represent
strategic component in such applications. The
burden of such requirements transfers to the VCOs,
which represent the core of the PLLs, as the indirect
frequency synthesis is the almost universal solution
adopted in TLC units. Thus, the VCOs have to deal
with the difficult trade-off among wide tuning
bandwidth and phase noise.
The state-of-the-art offers different design
techniques for wideband VCOs implementation,
such
as
frequency
translation
(division,
multiplication, injection locking), multiple VCOs,
switched inductors based VCOs, multiple inductors
based VCOs, transformer based VCOs, inductor
reuse based VCOs and magnetic tuning based VCOs
[3].
Distributed VCOs (DVCOs) obtain a wide tuning
range and good phase noise differently from ring
oscillators, which usually provide wide tuning range
and poor phase noise, and LC-VCOs, which provide
better phase noise but over smaller bands. The core
of a DVCO is the distributed amplifier (DA)
operating in the reverse gain mode, or in the forward
gain mode [4]. DVCOs are also known as travelling
wave VCOs which belong to the class of wavebased oscillators wherein there are the rotary-
ISBN: 978-1-61804-271-2
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Advances in Circuits, Systems, Signal Processing and Telecommunications
sum at each tap point on the drain (collector) line of
the DA, allowing a greater variation without the
switching-off of the oscillation. A suitable choice of
SL cell topology gives an additional degree of
freedom.
The proposed approach gives several advantages.
First, the characteristic impedance, Z0 , of the DA is
almost constant all over the tuning band. In addition,
a flat response is ensured over the entire tuning band
by the DA and, assuming that this latter has an
optimum noise figure at its center band, better phase
noise performances are obtained. The uniformity of
the performances in terms of output power, phase
noise and harmonics suppression into the overall
wide tuning range, achievable by using the proposed
solution, is a relevant feature for advanced
transceivers.
2 Theory of the Distributed VCO
The straightforward application of the
Barkahusen criterion to a DA brings to a structure
that concurrently governs phase and amplitude of
the signal along the path by interconnecting the gate
(base) and drain (collector) lines. Assuming equal
propagation properties for both transmission lines
into the DA, the oscillation frequency, fo , is [4]:
√
(1)
where vphase is the phase velocity along the
transmission lines, l is the electrical length of the
single cell, n is the number of transistors, L and C
are the inductance and the capacitance per unit
length and fC is the cut-off frequency of the loaded
transmission lines.
The oscillation frequency in (1) can be tuned
either changing the phase velocity and/or the
effective length of the transmission lines.
The losses in the DA limit, in practical
implementations, the number of transistors to 3-4.
Therefore, the DA operates at a frequency close to
fC and this condition implies that the characteristic
impedance of transmission lines strongly varies with
frequency, the attenuation of the transmission lines
due to impedance mismatch increases and the noise
figure of the DA increases as well.
These issues are circumvented when the DVCO
is divided into two blocks, the DA followed by a
Synthetic Line (SL) (Fig. 1) [13]. The resulting
DVCO shows a wide tuning range joint to small
variations of the output power, reduced phase noise
and low harmonic generation over the entire tuning
bandwidth [14]. It is critical to such arrangement
that the DA gives enough inverting gain to sustain
the oscillation over the required bandwidth,
according to its distributed nature, regardless of the
required phase shift. Therefore the transmissions
line cut-off frequency in the amplifier, fC,amp, must
be set far enough from the tuning band upper limit.
The phase shift required for the oscillation, 180°- α,
is controlled by the second block, where α is a small
phase shift introduced by the DA that can be
variable if the inherent varactor tuning technique is
used. The SL, in its basic version, is an m-cells
periodic structure, wherein each cell provides the
phase shift equal to (180°- α)/m.
The electrical behavior of the SL depends on the
topology of its basic cell. Since the tuning is
achieved by varying the electrical parameters of the
second block, it does not affect the in phase power-
ISBN: 978-1-61804-271-2
Fig. 1. DVCO topology.
2.1 General conditions of oscillation
The evaluation of the conditions of oscillation
requires to break the feedback loop, as in Fig.2. The
DVCO becomes the cascade of the DA and the SL
and the open loop gain is the product of the gain of
each stage. The DA contains n transistors and two
transmission lines. In the forthcoming paragraph we
assume a MOS implementation but similar
consideration can be made for the bipolar case. The
transistors amplify the forward wave traveling on
the gate line which is absorbed by the termination
matched to characteristics impedance of the gate
line, Zg. If the incident wave traveling on the drain
line travels with the same phase velocity, then at
each tap of the drain line the corresponding gain
stage gives an in-phase power contribution to the
signal. The backward wave on the drain line is
absorbed by the termination matched to
characteristics impedance of the drain line, Zd.
Assuming that the spacing between the transistors is
smaller than half wavelength then their input and
output impedances can be considered distributed
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Advances in Circuits, Systems, Signal Processing and Telecommunications
(
and added to the parameters per unit length of the
transmission lines. The DA gain can be calculated
starting from the circuit presented in Fig. 3.
(
)
(
)
(5).
)
By substituting in (5), (3) and (4), it is possible to
achieve the following expression:
(
(
)
)
(6).
Summing all the contributions, vo is expressed by:
(
(
∑
)
)
(7).
Using the identity, an - bn = (a-b)(an-1+an2b+..+bn-1), the previous equation becomes:
Fig.2. DVCO open-loop.
(
(
)
)
(8).
Finally, the DA gain is expressed by:
(
The impedance, Zk, seen at kth tap of the drain line
is Zd//ZSLK, where Zd is the characteristics
impedance of the drain line and ZSLK is the input
impedance of the SL transformed along the path to
the kth tap point along the drain transmission line:
(
)
)
(
where ΓSL is the reflection coefficient at the input of
the SL and γd is the complex propagation constant of
the loaded drain line. The voltage at the kth tap
point is:
(
)
(3)
where Gm is the large-signal transconductance of
each transistor. The voltage at the kth tap point of
the gate line is related to the gate line segment, lg,
and to the complex propagation constant of the
loaded gate line, γg :
(
)
(
)
(
(
)
(10).
)
)
(
(11)
)
where ΓL is the reflection coefficient at the output
section of the SL while γsl is the complex
propagation constant of the SL; the expression of γsl
depends on the type of cell into the SL.
The open loop gain is equal to ADA*ASL. In the
case of γglg = γdld = γl , the open loop gain is:
(4)
where vin is the voltage at the input node of the DA.
The voltage, vo , across the load ZSL can be
determined by using the superposition method. The
contribute to vo due to the kth transistor is:
ISBN: 978-1-61804-271-2
(9).
In the previous equations it has been considered the
case of a matched load Zd connected to the drain
line which absorbs the reflected wave. By using the
previous approach, it is easy to generalize the
expression of the DA gain when a generic load
impedance is connected to the drain line.
The gain of the second stage is the ratio between the
voltage, vo , calculated before, and vr (Fig.2). The
SL is a cascade of m identical cells, and can be
modeled as a transmission line. By using the
relation between the values of voltages along a
transmission line, it is possible to express as follows
the gain of the second stage:
) (2)
(
)
In the case of γglg = γdld = γl , the voltage gain is
equal to:
Fig.3. Equivalent circuit of the drain line.
(
(
)
(
28
)
(
)
(
)
(
)
(12).
Advances in Circuits, Systems, Signal Processing and Telecommunications
Finally the general condition of oscillation is
expressed by the following equation:
(
)
(
)
(
(
)
)
specs using the amplifier resource. This novel point
of view offers the possibility to implement new
tuning schemes thanks to the weak interaction
between the tuning controlled by the SL and the
operation of the DA [15]-[16].
Switched-capacitors banks are commonly used in
LC-VCOs design to achieve coarse jumps of the
capacitance C which fixes the oscillation frequency.
This variation, ΔC, is usually controlled by
exploiting a digital tuning scheme.
The insertion of a switched-capacitors bank,
similarly, gives to the SL of the DVCO the
capability of introducing a discrete variation in the
phase velocity along the transmission line (Fig.4).
The obtained variation operates a discrete change in
the band of synthesis. With this approach, the whole
tuning range is subdivided in a set of sub-tuning
ranges.
(13).
This expression sets both the amplitude and the
frequency of oscillation. In the case of γglg = γdld =
γl , the previous equation becomes:
(
)
(
)
(
)
(
)
(14).
The relation derived from the analysis presented
provides a good approximation of the oscillation
condition. This relation has been used to design the
DVCO presented in the next sections.
3 The tuning techniques
The most common tuning techniques used for
DVCO use the inherent-varactor control and delaybalanced current steering [4]. Other techniques are
the delay variation by positive feedback tuning
technique [6] and the current starving method [11].
The inherent-varactor tuning permits to vary the
oscillating frequency by modifying the phase
velocities along the gate (base) and drain (collector)
lines in the DA. The DC voltage bias controls the
active components in the two lines and its variation
in turn varies the capacitances along the lines, thus
inducing the desired phase-shift variation. This
solution is well suited for integration, because it
does not require external components. On the other
hand, the variations induced in the transistors bias
point are unacceptable when a wide tuning range is
required, because they usually bring to the damping
of the oscillation. Moreover, the capacitances in the
two SLs do not vary with the same rate when the
DC voltage varies, thus, generating a difference in
phase velocity which degrade the in-phase sum of
the contributions along the gain line. This condition
results in strong amplitude variations of the
oscillation in the tuning band. The delay-balanced
current steering tuning technique varies the effective
basic cell line length basing its operation on the
current-steering tuning technique. Usually this
solution is used for the fine tuning because it offers
less tuning span than the inherent-varactor
technique.
3.1
Fig. 4 Basic cell of the Synthetic Line.
The single cell of the synthetic line contributes by a
given phase shift, φSC , to achieve the required
oscillation frequency. When the banks of switchedcapacitors are added to the cells of the SL, they
participate to set the oscillation frequency, since the
cut-off frequency, fC,s.line , of the SL and, φSC depend
on the capacitances inserted by the banks,
√
) (
)
(15)
In particular, for a Π or T low pass cells φ SC is:
( )
(
) (16).
In (15), C(Vfine) is the capacitance provided by the
varactor in each cell, b0C1+b1C2+…+bk-1Ck is the
capacitance provided by each switched-capacitors bank
controlled by the digital tuning scheme (b i is the i-th bit
of the digital tuning signal VCOARSE). According to the
previous equations, VCOARSE controls the band of
operation while the oscillation frequency within each
sub-band is tuned by controlling the varactors inserted in
Alternative tuning techniques
Thanks to the separation between the amplification
and the phase shifting, the amplifier acts as a “loopgain tank” ensuring a wide bandwidth oscillation
capability. Thus, the SL design aims to meet the
ISBN: 978-1-61804-271-2
(
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Advances in Circuits, Systems, Signal Processing and Telecommunications
the cells of the SL.
This tuning solution aims to produce a variation in the
phase velocity along the transmission lines of the DVCO.
The theory introduced in the paper give good
performances in terms of wide tuning range, phase
noise, and harmonics suppression.
The concurrent availability of a wideband gain-tank
and versatile tuning techniques, like the switched
capacitors bank, represents an optimum starting
point for the design of multi-band DVCOs.
4 Prototype, measurements and results
The simplified prototype based on switched-capacitors
banks has a two-cells DA designed to ensure the required
loop-gain taking also into account the variation of the
input impedance of the SL due to the switching of the
capacitors banks. Each bank has one capacitor and
provides two different values of capacitance. Two
different bands, thus, are digitally selectable. The
measured DVCO measurements in Fig.5 feature more
than 360 MHz tuning span, from 1.52GHz to 1.88GHz.
The designed DVCO provides, at the same time, reduced
phase noise and a suitable filtering action of the
harmonics, assuring a good spectral purity. The subcharacteristics of tuning partially overlap to ensure the
complete frequency synthesis over the tuning range. The
prototype absorbs 8.5 mA from a 3.3V supply voltage.
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(a)
(b)
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GHz. (b) 1.69GHz to 1.88GHz
As expected from the theory, the prototype shows
uniform performances over the whole tuning range.
Comparing the results achieved by the DVCOs reported
in literature, summarized in Table I, with the results
provided by the proposed DVCO, summarized in Table
II, it is possible to note as this latter overcomes the other
DVCOs in terms of relative tuning range, demonstrating
the validity of the proposed technique.
5 Conclusion
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Advances in Circuits, Systems, Signal Processing and Telecommunications
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