Attenuators
Updated
October 29, 2012
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attenuators on EverythingRF.com
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Aten, the
Egyptian Sun God
that you attenuate with SPF45!
Here's a clickable index
our growing material on attenuators:
Carrottenuator (New for October 2012!)
Reflection
attenuators
Introduction
to attenuators
Fixed
attenuators
Lpad
attenuators
Clifton
Quan's patented attenuator
Temperaturecompensating
fixed attenuators
Power
dissipation in attenuators
Attenuator
math
Switchable
attenuators
Switchednetwork
attenuators
Switchedelement
attenuators
Digital
attenuators (stepped attenuators)
RMS amplitude and phase of switchable attenuators (new for August 2012!)
Variable
attenuators
Ray
Waugh's PIN diode attenuator (new for June 2011!)
Gain
equalizers
Introduction
to attenuators
Attenuators are passive
resistive elements that do the opposite of amplifiers, they
kill gain. Why would you want to do that? Suppose your design
specification calls for 10 dB gain, with a 1.2:1 maximum VSWR.
You search the amplifier vendors, and locate an amplifier
in your frequency band, but it has 14.5 dB gain and a lousy
2.5:1 match on the input. By adding an attenuator to the input,
you can bring the gain down to 10 dB, and you will be improving
the input match. Two things to consider when you play this
game: don’t add an attenuator to an amplifier’s input if you
are concerned with the amplifier’s noise figure, every dB
of attenuation you put on the input will raise the noise figure
by the same amount. Similarly, don’t add an attenuator to
a power amplifier’s output without considering what it will
do to your output power, or what the RF output power of the
power amp might do to your attenuator.
There are five common attenuator
topologies used in microwave circuits, the tee, the pi, the
bridged tee, the reflection attenuator and the balanced attenuator.
The tee, pi and bridged tee each require two different resistor
values, while the reflection and balanced attenuators need
only a matched pair of resistors. This allows both the reflection
and balanced topologies to be used as variable attenuators
with a single control voltage or control current. There are
two variations of the reflection attenuator, depending on
whether the terminations R_{1} are less than or greater
than the system characteristic impedance Z_{0}.
When would you use a tee
versus a pi versus a bridged tee? Here's some examples. When
you are designing a fixedvalue 3dB attenuator on a thin
film circuit, with a sheet resistivity fixed at 100 ohms per
square, the 8.5 ohm value of R_{1} for a tee might
be a little hard to accurately etch, and the pi might be a
better choice. On the other hand, if your sheet resistivity
was 10 ohms per square, you'd need 29 squares to create R_{1}
for the pi, and that might prove to be too inductive to work
at high frequency. With thick film circuits, you can take
your pick because there are different resistivity values available.
The bridged tee can be
thought of as a modified pi network. The attraction to the
bridged tee comes when you are making a variable attenuator,
with PIN diodes or FETs. Here are two reasons you might consider
it over the pi. First, it only needs two variable resistors
(pi and tee need three). Second, the bridged tee uses the
full range of resistor values, from zero to infinity, for
both R_{1} and R_{2}. For the pi attenuator,
R_{1} never goes below Z_{0} (50 ohms) so
some of the diodes' useful resistance range is wasted. Finally,
the bridged tee has a tendency to match itself to Z_{0}
at high attenuation values, because of its two fixed resistors.
In practice, the pi may give you higher attenuation range.
The resistor R_{2} can be a "sneak path"
in the bridged tee because the diode (or FET) never reaches
zero ohms.
The table below provides
equations for solving for the attenuator resistive elements. It is incomplete; did you know that the tee and pi attenuators alone can have twelve forms of these equations, each? Think about this: there are four variables (Z0, R1, R2, and dB) and only two must be chosen to lock in the other two.
Attenuator equations

Configuration

R_{2}
vs. R_{1} 
R_{1}
vs. Attenuation 
R_{2}
vs. Attenuation 
Tee
Attenuator




Pi
Attenuator




Bridged
Tee Attenuator




Reflection
Attenuator,
R1
<Z0




Reflection
Attenuator,
R1>Z0




Balanced
Attenuator




Click on the calculator
icon ()
to check out our calculator where you'll be able to enter
your desired attenuation parameters and we will calculate
the resistors for you.
If you use the above equations
to calculate R_{1} and R_{2}, be sure to observe
whether "ATT" is divided by 10 or 20. For those
of you too busy or lazy to calculate your own resistor values,
the table below should be useful (Z_{0} is assumed
to be 50 ohms, but you can scale the values if necessary).
New for June 2012:
Turns out for the tee, pi and bridged tee attenuators, there are four parameters: R1, R2, Z0 and dB. If you pick any one of them, the other two can be solved. Why would you want to pick dB and Z0 instead of R1 and R2? Trust us, there are situations where that would be useful. Of course you can iterative solve any of the equations to get the answers you seek, but why not come up with elegant, closed form equations?
There are twelve possible equations for each attenuator type. We have completed the solutions for the tee, and much of the pi attenuator. Below we post the solutions. If someone can help us finish the missing ones we'd appreciate that! You can cut and paste them into Excel and verify that they work, or ask us nicely for a spreadsheet that already has them in it!
Tee attenuator  twelve equations
Pick R1, R2:
dB=20*LOG(SQRT(R1^2+2*R1*R2)+R1)20*LOG(SQRT(R1^2+2*R1*R2)R1)
Z0=SQRT(R1^2+2*R1*R2) 
Pick R1, Z0:
R2=(Z0^2R1^2)/2/R1
dB=20*LOG(Z0+R1)20*LOG(Z0R1) 
Pick dB, R1:
R2=2*R1*(10^(dB/20)+1)*(10^(dB/20))/(10^(dB/10)1)/(10^(dB/20)1)
Z0=R1*(10^(dB/20)+1)/(10^(dB/20)1) 
Pick R2, Z0:
R1=SQRT(R2^2+Z0^2)R2
dB=20*LOG(Z0+SQRT(Z0^2+R2^2))20*LOG(R2) 
Pick dB, R2:
R1=2*R2/((10^(dB/20)+1)^2/(10^(dB/20)1)^21)
Z0=(R2/2)*(10^(dB/10)1)/10^(dB/20) 
Pick dB, Z0:
R1=Z0*(10^(dB/20)1)/(10^(dB/20)+1)
R2=2*Z0*10^(dB/20)/(10^(dB/10)1) 
Pi attenuator  twelve equations
Pick R1, R2:
Coming soon!

Pick R1, Z0:
R2=2*Z0^2*R1/(R1^2Z0^2)
dB=20*LOG((R1+Z0)/(R1Z0)) 
Pick dB, R1:
Coming soon!

Pick R2, Z0:
R1=(Z0^2+Z0*SQRT(Z0^2+R2^2))/R2
dB=20*LOG((R2/Z0)+SQRT((R2/Z0)^2+1)) 
Pick dB, R2:
Coming soon!

Pick dB, Z0:
R1=Z0*(10^(dB/20)+1)/(10^(dB/20)1)
R2=(Z0/2)*(10^(dB/10)1)/10^(dB/20) 
Fixed
attenuators
There are many commercially
available fixed attenuators, including chip, coaxial, and
waveguide implementations. Two considerations you will need
to consider are frequency of operation, and power handling.
Chip attenuators can dissipate
hundreds of milliwatts up to a few watts. The higher power
units will be realized on thermally conductive substrates
such as beryllium oxide and aluminum nitride.
If you are designing your
own attenuator, the resistive elements can be realized with
either thick film or thin film processes. While the thick
film process can use different "inks" for different
resistors, providing different ohm/square values, the thin
film process uses one sheet resistance for all resistors.
Having different inks solves the problem of making compact
resistors of two radically different values, for instance,
a 1 dB tee attenuator would require an R_{1} of 2.9
ohms and an R_{2} value of 433 ohms. Large value thin
film resistors can be made compact by using a meandered layout.
In both thick and thin film processes, the "asfired"
tolerance is usually no better than 15%. Both types of resistors
can be trimmed with a laser to tolerances of less than 1%
(see also
thin film resistors).
There are two opposing
concerns in microwave attenuator design: the high frequency
of operation requires that resistive elements be kept small
to be considered "lumped
elements" (i.e. less than 1/10 wavelength), and power
handling requires that resistors be made as large as possible
to dissipate heat. The heat issue can be dealt with for small
resistors if attention is paid to the material properties
of the resistors’ substrates and attachment methods, i.e.
beryllium oxide for a substrate instead of alumina and solder
attachment instead of conductive epoxy (see also material
properties and heat
dissipation).

Rule
of thumb: a chip attenuator is good for at least 1/16
watt if it is mounted to a circuit card such as Duroid
or FR4, 1/4 watt if mounted to metal with conductive
epoxy, and 1/2 watt if it is attached with solder to a
metal heatsink. 
