Updated July 9,
here to go to our main page on phase shifters
here to go to our page on switched filter phase shifters
to go to our page on filters
here to go to our main page on lumped elements
New for January 2009!
We now have a spreadsheet that performs the calculations described
below, it is described on
its own page.
On this page we show the exact
calculations for tee and pi lumped element filters to achieve
any phase shift for any frequency and characteristic impedance.
If a constant phase shift is
desired over a wide frequency range, the switched
line phase shifter isn't going to cut it. A high-pass/low-pass
phase shifter can provide near constant phase shift over an octave
or more. By "high-pass/low-pass" we refer to the fact
that one arm forms a high-pass filter while the opposite arm forms
a low-pass filter. A second advantage of the high-pass/low-pass
phase shifter is that it offers a very compact layout because lumped
elements are typically used instead of delay lines. This is an important
consideration for "low frequency" designs (i.e. below
X-band) because delay transmission lines can be quite large. The
cutoff frequencies of the two filter networks obviously must be
outside of the phase shift band for this scheme to work.
The figure below shows predicted
phase response for a high-pass/low-pass 90-degree phase lumped-element
shifter optimized for C-band operation.
phase shifter, C-band 90 degree bit
Referring to the schematic below,
the values of the lumped elements in the simulation are C1=1.40
pF, L1=2.09 nH, C2=0.40 pF, and L2=0.63 nH; these were determined
using the optimizer within Agilent's ADS simulator to achieve the
flattest phase response from 4 to 8 GHz. This is an ideal phase
shifter, switch insertion phase contributions were neglected in
the simulation. High-pass/low-pass phase shifters usually require
two control signals to throw the switches (we'll discuss some that
don't need two switches one of these days). Between 4 and 8 GHz
the phase shift (green trace) stays within -90 to -99 degrees, a
nearly flat response that is not possible from a switched line phase
shifter. By our Microwaves101 convention, the high-pass arm provides
the reference state, as it provides the least-negative insertion
In practice, the distinction
between switched-line and high-pass/low-pass phase shifters is blurred.
Lumped capacitors are employed in the filter networks, but the inductors
are really just transmission lines of high characteristic impedance.
High-pass/low-pass phase shifter topology with tee networks
By the way, you'll
find similar schematics in a Word document you can get for free
in our download area, it's
called Electronic_Symbols_xx.doc, where xx is the revision number.
exact lumped element values
In the preceding
example, an optimizer was used to determine the L and C values.
But you can use simple math to come up with values that will give
you the exact result at center frequency, then optimize the values
over your frequency band if you prefer.
You have two equivalent
choices for each filter, the tee or the pi; your decision might
be driven by whichever one offers a more compact layout, or perhaps
one network will violate a design rule for minimum capacitor size.
Below are annotated schematics to reduce confusion. Note that you
could use more lumped elements than the three shown, but usually
three elements will work just fine. Actually, the low-pass network
can be approximated with just a high-impedance transmission line,
in this case you only need one element!
for the ideal lumped element values. For a phase bit with
phase shift, use /2
in the equations to obtain half of the phase shift from each network.
We've lost the derivation for these equations, the first person
that shows us how they were derived will win a nice crisp twenty
dollar bill! One textbook reference
for these equations (in a slightly different form) is Robert Weber's
Introduction to Microwave Circuits.
Note that phase
is in radians when you use Excel.
Below are exact
lumped element values for four different bits at 6 GHz (which of
course we calculated in a spreadsheet!) You can scale the L and
C values as 1/frequency, or make your own spreadsheet, or wait for
us to post ours one of these days. Remember that each filter provides
half the desired phase shift, i.e. the LP filter for 22.5 degrees
provides 11.25 degrees (negative) phase.
The table below
was corrected on January 6, 2009, thanks to Jim!
Now let's compare
inductor and capacitor values from the equations to the preceding
example that arrived at values using an optimizer, for the 6 GHz,
90 degree bit using tee networks. They are pretty close!
We often get feedback
from engineers on the inability to obtain inductor and capacitor
values of nonstandard values.
Most phase shifter designs are in monolithic microwave (MMIC) format,
where you can create any value lumped element you want, subject
to size constraints and the ability to deal with parasitic effects.
out our spreadsheet that performs the lumped element value calculations
and plots the response over frequency!
phase shifter example 1
Let's look at a
MMIC phase shifter that employs the lumped element technique at
35 GHz, TriQuint's TGP 2104. While we're on the subject, we write
"a MMIC" instead of "an MMIC" because we pronounce
the acronym "mimic", not "M-M-I-C", can you
IEEE cats dig that?
are comprised of series switch FETs with the gate fingers aligned
vertically. By floating the FETs to +5 volts (supplied by pad "V2")
the control voltage (V1) is positive (0 or 5 volts) instead of the
normal negative voltage associated with switch FETs. There is a
lot of stuff you can't see in the die map, including several high-value
resistors that complete the bias network; somewhere there must be
an "inverter" to supply complimentary logic to two of
the switch FETs; you can't see the blocking caps on the input and
output RF lines, they are built into the RF paths. There are visible
ESD protection diodes at each of the bias pads, connected to the
ground vias of the right side RF probe point.
The low-pass network
is on the north side of the chip and uses the tee topology, the
high-pass network is on the south side and also uses the tee topology.
The calculated values for L1, C1, L2 and C2 are 0.227 nH, 0.091
pF, 0.227 nH and 0.091 pF respectively. Did we mention that for
the ideal 180 bit calculation, the L's and C's are the same for
the HP and LP networks?
In many real phase
shifters you'll find that more than 50% of the phase shift is done
in the low pass network and less than 50% in done in the high pass.
Why? It just seems to give better bandwidth! That is exactly what
is going on in the TGP2104. The series inductors in the LP network
are longer than the shunt inductor in the HP network. So the LP
network contributes perhaps -135 degrees phase shift while the HP
network contributes +45 degrees.
This phase shifter
bit has about 4 dB loss which is undesirable but understandable.
This loss is caused primarily by the switch FETs. As you go up in
millimeterwave frequencies, switch FET sizes must be reduced to
minimize their parasitic off-capacitance, which increases their
So, what are those
three tiny trombones on the inductors? These allow TriQuint engineers
to mess around with the design in the lab to optimize the response
by cutting and smooshing metal. Even though they own the
GaAs foundry and the models, TriQuint girly-men often resort
to this tedious trick. You'd think that they would remove the leftovers
before they create a production mask (or data sheet.) Way to go,
instilling modeling confidence for the rest of your foundry customers!
More to come!