Resistive
power splitters
Revised December 23,
2013
Click
here to go to our main page on couplers and splitters
Click
here to go our page on resistive taps.
Click
here to check out the Chris Owen's resistive unequal splitter
Click
here to check out Greg Adams' resistive unequal splitter
New for December 2013: we have information from Andy on additional degrees of freedom with resistive splitters:
We at TEGAM were designing an amplifier test bench and had occasion to look on your site for some splitter design input. I was intrigued with the approach taken by Adams at www.microwaves101.com/encyclopedia/Resistive_splitter1.cfm but really wanted to be able to control the attenuation to both output ports. After a bit of fiddling, I came up with a two output port splitter design calculator that lets you set the attenuation to each port (within practical limits). The derivation and calculator are attached in the files names, “Two Output Four DOF”.
In a further step, our design needed a splitter with two equal outputs and a third monitoring output with some “nice” ratio to the others. That was a relatively simple step and is attached as “Three Output Four DOF”.
Go to our download area and grab the Zip file that contains these analyses. Thanks, Andy!
Wye and Delta equalsplit resistive
splitters
If you need an unequal split,
check out the Owen and the Adams splitters (links above). Use the
Owen splitter for maximum isolation, or the Adams splitter for highest
efficiency. The Wye and Delta provide equal split.
Resistive power dividers are
easy to understand, can be made very compact, and are naturally
wideband, working down to zero frequency (DC). Their down side is
that a twoway resistive splitter suffers 10xlog(1/2) or 3.0103
dB of real resistive loss , as opposed to a lossless
splitter like a hybrid. Accounting for 3.0103 dB real loss and 3.0103
dB power split, the net power transfer loss you will observe from
input to one of two outputs is 6.0206 dB for a twoway resistive
splitter, so they are often called 6 dB splitters. Dig?
For applications where loss is
critical such as power amplifier combiners, the extra loss of a
resistive splitter is an unacceptable compromise. But in others,
especially in test equipment where power is just an outlet strip
away, resistive splitters have their place.
For the 2way resistive dividers
shown below, one half of the power that flows through it is wasted
in the resistors. For example, a one watt signal at port 1 will
result in two quarterwatt signals at ports 2 and 3 (down by 6
dB). Because of the loss within the network, you have to carefully
consider the power dissipation and resistor power ratings. You can
put many watts through a "lossless" divider such as a
ratrace or branchline coupler. But a watt might burn out a resistive
divider. Another disadvantage it the none of the ports are truly
isolated from each other.
It's time for a Microwaves101
rule of thumb!
The isolation of a resistive splitter is equal
to its insertion loss. The 6 dB threeport splitter has (ideally)
6.02 dB loss from any one port to any other port (S21=S31=S23).
The advantages of resistive dividers
are size (it can be very small since it contains only lumped
elements and not distributed elements), and they can be extremely
broadband. Indeed, a resistive power divider is the only splitter
that works down to zero frequency (DC). It's so broadband, that
we didn't even bother to make a frequency response plot for you!
Below are schematics of the two
options for threeport resistive splitters, the "delta"
and the "wye". Resistor values as shown will ensure that
each port is impedance matched to Z_{0}. These schematics
and many others are available in a Word file that you can get in
our download area, it's called
Electronic_Symbols.doc. You'll find it comes in handy for creating
simple block diagrams in Word, PowerPoint or Excel.
Delta 6 dB resistive
splitter
Wye 6 dB resistive
splitter
New for August 2012: Let's take some time to analyze the wye splitter. First, let's label all of the resistors R1 so we can better keep track of things.
In order for all ports to be matched, the three resistors must be the same, so we gave the value R1.
The impedance looking into each port must be matched to Z_{0}. Looking into Port 1, the impedance Z_{in} must equal Z_{0}:
Z_{in}=Z_{0}=R_{1}+(R_{1}+Z_{0})^2/(2R_{1}+2Z_{0})
This can be solved pretty quickly, with the following advice: first subtract R_{1} from both sides, them multiply both sides by 2*(R_{1}+Z_{0}). You will soon find out that R_{1} must equal Z_{0}/3 to match the three ports.
Nway resistive
splitters (equal split)
You can make Nway resistive
splitters easily from the Wye splitter. The Delta resistor becomes
a nightmare network for more than a twoway split, it can't be constructed
in two dimensions.
The appropriate resistors for
an Nport Wye splitter are found by the equation:
R=Z_{0}x(N1)/(N+1)
For examples, a threeway splitter
needs resistors of Z_{0}/2, while a fourway splitter needs
resistors of 3xZ_{0}/5, and so on.
The efficiency of a resistive
splitter gets worse and worse the more arms you split to. The transferred
power ratio is (1/N)^2, as opposed to a lossless splitter that varies
as 1/N. So for a fourway splitter, only 1/16 of the power makes
it out to one of the four matched loads. It's time for another Microwaves101
rule of thumb!
To put it simply, the resistive splitter has
double the dB loss compared to a lossless splitter's insertion
loss. Thus a twoway resistive splitter transfers 6.02 dB power
to each arm, a threeway splitter transfers 9.54 dB, a fourway
transfers 12.04 dB, etc. An infiniteway resistive splitter would
lose 100% of the incident power and transfer nothing to the loads!
Fractional
dissipation in the Wye resistive splitter
New for February 2007!
We've solved this algebra problem for the Wye splitter, here it
is. If the resistor closest to the common port is designated "resistor
A" and the other two resistors are designated "resistor
B" and "resistor C" then:
Power dissipated in resistor
A:
PDissA=Pin x (N1)/(N+1)
Power dissipated in B and C are
equal by symmetry.
PDissB=Pin x (N1)/[(N+1)xN^2)]
Let's tie it all together. The
table below shows the fractional dissipation and the output powers.
The "power factor" is a measure of the efficiency of the
network, it is the sum of all the output powers divided by the input
power.
N 
PDissA 
PDissB or PdissC 
Pout 
Power factor 
2 
33.3% (4.77
dB) 
8.33% (10.79
dB) 
25% (6.02 dB) 
50% (3.01 dB) 
3 
50% (3.01 dB) 
5.56% (12.55
dB) 
11.1% (9.54
dB) 
33.3% (4.77
dB) 
4 
60% (2.22 dB) 
3.75% (14.26
dB) 
6.25% (12.04
dB) 
25% (6.02 dB) 
5 
66.7% (1.76
dB) 
2.67% (15.74
dB) 
4% (13.98 dB) 
20% (6.99 dB) 
6 
71.4% (1.46
dB) 
1.98% (17.02
dB) 
2.78% (15.56
dB) 
16.7% (7.78
dB) 
Fractional dissipation in N=2
Delta resistive splitter
We only use the delta splitter
for N=2, it doesn't make sense for higher order splitters because
it becomes a 3D nightmare.
The fractional dissipation in
an N=2 delta splitter is easy to calculate. The resistors that are
in series with the split ports dissipate as much power as the two
outputs. If the series resistors are labeled "resistor A"
and the resistor that shunts the output ports is "resistor
B", then the dissipation is given by:
N 
PDissA 
PDissB 
Pout 
Power factor 
2 
25% (6.02 dB) 
0 
25% (6.02 dB) 
50% (3.01 dB) 
Send us your comments!
