th. Inductance tuning is realized through the effect of
mutual inductance. As a demonstration prototype, a single unit
cell and two cascaded unit cells were implemented in 90nm
digital CMOS process. Delay values ranging from 14ps 40ps
were obtained from DC to 8GHz while maintaining matched
condition over the bandwidth with delay variations of less than
±%5. These delay cells could be used in broadband impulse-
based beamforming systems to provide variable delays in each
RF path.
Index Terms Phase shifter, passive delay element, variable
delay, synthesized transmission lines, inductance tuning, induc-
tance multiplication.
I. I
NTRODUCTION
Delay elements are important building blocks of numer-
ous circuits and systems such as broadband beamforming
antenna arrays, delay locked loops, delay based oscillators,
and equalizers. Accuracy, tunability and immunity to process-
voltage-temperature variations are key performance metrics in
designing delay cells.
Various forms of active and passive delay elements have
been used previously [1]- [3]. In systems using active delay
elements, the delay accuracy is maintained through a feedback
system and accurate external reference. Active delay cells
could be realized in small footprints but they dissipate power
and have limited bandwidth whereas passive delay lines could
be accomplished with high bandwidth and good accuracy
determined by inductances and capacitances that are highly
accurate compared to active delay elements.
The inductance value is mainly a function of lateral di-
mensions of an inductor which is determined by a pre-
cise lithographic process. Inter-digitated MOM (Metal-Oxide-
Metal) nger capacitors using multiple layers of metals and
exploiting intermediate via capacitances are quite precise.
These structures are immune to process variation due to
the large amount of inherent averaging done on small local
capacitances in comprising the desired capacitor. Unlike active
delay cells, passive elements are largely independent of voltage
and temperature variations.
A new method to obtain broadband and tunable delay
out of synthesized transmission lines based on an inductance
multiplication technique is introduced in this paper. In section
II we discuss different types of passive delay structures.
Section III focuses on the inductance multiplication technique.
Implementation and measurement results are presented in
section IV.
II. P
ASSIVE
D
ELAY
L
INES
As shown in Fig. 1a, the most straightforward way to
implement a delay element is to use a transmission line.
To create a variable delay, multiple transmission lines of
different length can be switched into the signal path. On-chip
transmission lines are highly accurate, completely linear and
very broadband. However they consume large amount of chip
area, and are therefore too costly for commercial applications
below 10GHz.
To decrease the size, articial transmission lines can be
used. In these synthesized transmission lines, lumped inductors
and capacitors mimic the role of distributed inductance and
capacitance in a real transmission line. The conventional way
to make the delay of a synthesized transmission line tunable
is by means of varactor loading (Fig. 1b). Varying the line
capacitance changes the wave velocity and hence the delay
(T
D
= LC) of the line. However this comes at the expense
of changing the lines characteristic impedance (Z
o
=
L
C
).
To maintain good return loss, delay variations of only a small
fraction of the nominal delay is acceptable.
To overcome the Z
o
variation problem, in [4] a variable
capacitor is added in series with the inductor (Fig. 1c).
By varying this capacitance, the effective reactance of the
series LC circuit is altered. This effective reactance tunability
compensates for the Z
o
variation caused by the change of
capacitance values in shunt varactors. Since in this technique
a series LC network is emulating the effect of a variable
inductor, its functionality is limited to a small bandwidth,
and therefore is suitable for narrowband signals. To make an
articial varactor loaded transmission line work with wideband
signals, the actual inductance value should be adjusted instead
of the effective series reactance, as shown in Fig. 1d. If
both series inductance and shunt capacitance are tunable, the
delay could be varied while maintaining constant Z
o
. In the
next section, various techniques to realize tunable inductors
are described and their advantages and disadvantages are
highlighted.
III. I
NDUCTANCE
M
ULTIPLICATION
Inductance is determined by the geometry of a closed
path of current and the permeability (µ) of the surrounding
978-1-4244-1808-4/978-1-4244-1809-1/08/$25.00
© 2008 IEEE
2008 IEEE Radio Frequency Integrated Circuits Symposium
RTU1E-1
445 (a)
(b)
(c)
(d)
Fig. 1.
(a) Switched transmission lines (large footprint). (b) Varactor loaded articial transmission line (Z
o
variation). (c) Modifying the effective series
reactance by adding a varactor in series with the inductor (narrowband network). (d) Broadband solution for tunable synthesized transmission lines presented
in this paper.
material. In traditional IC processing, magnetic materials of
high permeability are not available and therefore the only way
to change the self inductance of a single loop is to change the
geometry, which implies that the path of the current or return
current ow should be recongured. It is not trivial to change
the geometry of a an inductor electronically and efciently
since switches incur substantial loss.
The other way to change the effective inductance is to
change the net magnetic ux passing through a loop via the
ux generated by another loop. This could be done via a
transformer if the current passing through the secondary loop
is controlled. As depicted in Fig. 2, if the current passing
through the secondary is a multiplicative copy of the primary
current (I
2
= n · I
1
), then the effective inductance seen
through the primary is L
ef f
= L
1
+ n · M . Therefore either
the secondary current or the mutual inductance should be
adjustable in order to have a variable inductance at the primary.
In Fig. 3 several methods to change the magnetic ux of
the primary loop are depicted. In Fig. 3a-c, signals are single-
ended, and therefore an input balun is used to convert the
signal from single-ended to differential and to produce a copy
of the current owing in the primary. A multiplication of this
current will be routed into the secondary to change the net
magnetic ux crossing the primary loop.
The structure depicted in Fig. 3a uses a current amplier
to adjust the current at the secondary. In this structure, the
secondary current could be varied over a wide range but it
comes at the price of DC power consumption and limited
bandwidth due to the fact that the operation frequency should
be reasonably below f
t
/(N + 1). Furthermore, if the current
amplier is implemented with reasonable power consumption,
its input impedance (1/g
m1
) will be high and it needs a
matching network to lower it down to the characteristic
impedance of the top path. Otherwise if the impedance looking
into the current amplier is much higher than the impedance of
delay cell (Z
o
), the voltage will appear mostly on the current
amplier side rather than at the input of the delay cell. This
Fig. 2.
Inductance tunability, net magnetic ux crossing a loop is altered
via the ux generated by another loop.
results in a signicant attenuation for the signal that appears
at the output of the delay cell.
Fig. 3b demonstrates another structure that modies the
magnetic eld induced in the primary by changing the number
of turns of the secondary inductor. Since M = kL
1
· L
2
,
changing the inductance of the secondary modies the mutual
inductance and as a result the effective inductance of the
primary loop. Unlike the previous conguration, this structure
does not consume any DC power, however large inductance in
the bottom path lowers the bandwidth. Furthermore, changing
the inductance at the bottom path alters its impedance, which
loads the input balun. Variable loading results in variable
voltage levels that appears at the input of the delay cell, and
this causes the signal to experience variable gain from input to
the output depending on the inductance needed for each delay
setting.
In the structure shown in Fig. 3c, the magnitude of the
current and the inductance of the secondary loop stay un-
changed. However with the aid of switching network, current
will change direction in the secondary and in one switching
condition it totally bypasses the secondary and directly goes
into the termination resistor. Hence the effective inductance
of the primary will take on values of L
1
M , L
1
, and
L
1
+ M . If the mutual inductance is designed to be half
the value of self inductance, then the effective inductance
446 (a)
(b)
(c)
(d)
Fig. 3.
Four different ways to realize inductance tuning: (a) Using a current amplier, (b) varying the mutual inductance, or by rerouting the current in the
secondary in a (c) single-ended or (d) differential manner.
looking into the primary will have a ratio of L
max
/L
min
=
(L + M )/(L M ) = 3. To have a constant Z
o
, the same
tuning range should apply to the capacitors: C
max
/C
min
= 3,
yielding a delay variation factor of three while maintaining
constant Z
o
, which is considerably higher than the achievable
delay variation of a varactor loaded synthesized transmission
line.
The circuit in Fig. 3c has no DC power consumption, and
the bottom path does not impose bandwidth limitations on the
top (delay) path, and there are no