Owen resistive splitter

Updated November 27, 2007

Click here to go to our main page on resistive splitters

Click here to go to our page on L-pads

Click here to check out the Adams unequal resistive splitter, it offers less loss that the Owen splitter but lower isolation between arms (and it doesn't offer 3-way or higher splits)

New for May 2007! This idea for this content was contributed by Chris Owen, who designed this cool splitter. No where else in the universe but Microwaves101 will learn about this, thanks to Chris who chose to "publish" it here!

New for December 2007: here's an example of an Owen splitter!

The Owen splitter provides multiport capability (2-way to N-way), with unequal splits possible to any of the ports. Like all resistive splitters it offers wideband performance. What sets this splitter apart from others (wye, delta, and the Adams splitter) is that the Owen splitter achieves maximum output to output isolation because none of the resistors are in the common path. In this respect there is no better resistive splitter!

Why would you want to consider this power splitter? Everything in engineering is a tradeoff. Here's the pros and cons:

1. Like all resistive splitters, the only limitation on bandwidth is due to parasitic elements, there is nothing intrinsic to the design that would limit bandwidth.
2. It is simple to expand the design from 2-way to 3-way to 4-way to N-way. But with increasing N, the efficiency is reduced.
3. Like all resistive splitters, you will incur "real" loss when you use it. It is actually lossier than classic wye and delta resistive splitters described here.
4. It provides better isolation between split ports than classic wye and delta splitters.
5. It provides a means to vary the voltages of the signals of split ports, so it can be used as an unequal splitter.

We envision this design as a wideband equal splitter on a thin-film or thick-film chip, with 2-way, 3-way and 4-way versions. Anyone interested, give us a shout!

Here's the description Chris sent us in January 1007:

In a semiserious fashion I wish to lay claim to the Owen Resistive Splitter (similar to the Wilkinson splitter!) if it hasn't already been claimed, I have never seen it elsewhere.

This particular resistive splitter design provides 10 dB power loss from the input to both outputs, maintains 50 ohms match on all ports, AND provides 19 dB of isolation between each of the splitter outputs.

This splitter design may be useful for wideband applications (dc to 18 GHz!) where attenuation is not an issue and where a little isolation is useful and where simplicity and low cost and low space are also important.

Chris's splitter is based on L-pad attenuators.

Unequal split, two-way Owen splitter

Below is a schematic for a 2-way Owen splitter with the ports defined. Port 1 is the common port, as a divider this is where the incident signal enters. We'll use this resistor nomenclature (R1, R2, R3 and R4) in the analysis below.

Let's review what is meant by coupling factor and isolation. We (Microwaves101) define coupling factor as the ratio of the output voltage at a coupled port to the voltage incident on the common port, which we will call (port 1):

Most often the coupling factor is expressed in dB, which is 20xlog(CF).

The power factor is the square of the coupling factor:

PF in dB is 10xlog(PF), at which point the coupling factor and power factor are identical.

Isolation is the ratio of voltage incident to a coupled port to another coupled port. For a two-way splitter the isolation from port 2 to port 3 is:

The isolation from port 2 to port 3 is merely the sum of the coupling factors of these two ports (you can prove that for a homework!) This is why the Owen splitter offers the maximum isolation of any resistive splitter.

The efficiency factor is a measure of the efficiency of the device. It is the power output at all of the coupled ports divided by the power input at the common port. Expressed in terms of the coupling factors the efficiency is:

Now it's time to solve some equation equations for resistor values. The two-way, unequal Owen splitter resistor values can be solved by choosing one resistor and solving for the rest, noting that all ports need to be matched to 50 ohms. We'll skip the painful algebraic steps that get you to the solution, for this you'll need a large pad of paper, two cups of coffee and a #2 Pokemon pencil if you're anything like the rest of us... R₂ can be expressed in terms of the coupling factor of its arm:

We solved the equations for R₁, R₂, R₃ in terms of R₂:

And last, we present equations for the two coupling factors in terms of resistors that make up their arms:

All of this stuff is great material for a spreadsheet, we've been there and done that. If anyone is interested, ask us nicely and we'll share it with you. Here's a plot of the four resistor values for unequal splits and Z₀=50 ohms, versus the ratio of the two coupling factors (in dB):

Below is a table of coupling factors, isolation and resistor values for 2-way Owen splitter (Z₀=50 ohms). Looks like you can never get less than 19 dB isolation with the Owen splitter! You can't say the same thing about the Wilkinson splitter. The efficiency () is theoretically equal to 100% when all of the power is coupled to one of the arms (which would not be a useful coupler.) Efficiency bottoms out at about 22% for intermediate coupling values.

Update August 2007: previously the data in R1 and R2 columns was inadvertently reversed, it's fixed now. Thanks to Robert!

CF2	CF3	CF2/CF3		Isolation	R1	R2	R3	R4
(dB)	(dB)	(dB)	(%)	(dB)	Ohms	Ohms	Ohms	Ohms
-1	-30.57	29.57	80%	-31.57	5.77	869.55	843.81	53.05
-2	-24.32	22.32	63%	-26.32	11.61	436.21	409.69	56.47
-3	-20.58	17.58	51%	-23.58	17.61	292.40	265.06	60.31
-4	-17.89	13.89	41%	-21.89	23.85	220.97	192.78	64.62
-5	-15.76	10.76	34%	-20.76	30.40	178.49	149.42	69.46
-6	-14.01	8.01	29%	-20.01	37.35	150.48	120.49	74.88
-7	-12.53	5.53	26%	-19.53	44.80	130.73	99.82	80.97
-8	-11.24	3.24	23%	-19.24	52.84	116.14	52.84	87.80
-9	-10.10	1.10	22%	-19.10	61.59	104.99	72.18	95.46
-9.54	-9.54	0.00	22%	-19.08	66.67	100.00	66.67	100.00
-10	-9.10	-0.90	22%	-19.10	71.15	96.25	62.48	104.06
-11	-8.20	-2.80	23%	-19.20	81.66	89.24	54.52	113.70
-12	-7.39	-4.61	25%	-19.39	93.25	83.54	47.87	124.53
-12	-6.66	-6.34	27%	-19.66	106.07	78.84	42.24	136.67
-14	-6.01	-7.99	29%	-20.01	120.31	74.93	37.41	150.30
-15	-5.41	-9.59	32%	-20.41	136.14	71.63	33.23	182.74
-16	-4.88	-11.12	35%	-20.88	153.78	68.83	29.58	182.74
-17	-4.39	-12.61	38%	-21.39	173.46	66.45	26.37	201.99
-18	-3.95	-14.05	42%	-21.95	195.43	64.40	23.54	223.58
-19	-3.55	-15.45	45%	-22.55	220.01	62.64	21.03	247.81
-20	-3.19	-16.81	49%	-23.19	247.50	61.11	18.80	275.00

Two-way Owen splitter layout

Here's an excellent layout for a "wideband" two-way Owen splitter, this image was contributed by Chris Owen himself. Note that the four resistors are all located as close to each other as possible, and as close to the common node as possible. Any significant track length between the resistors acts as distributed transmission line which will cause a phase shift; at higher frequencies the increasing phase shift will eventually skew the response (coupling factors will shift and port VSWRs will increase). At some frequency any transmission line will become 1/4 wave and then all bets are off!

The grey/black circles represent vias that tie the backside ground to the topside grounds.

N-way, equal coupling factor Owen splitters

Here the arms would all have the same resistor values, R₁ and R₂. After some math, the formulas for R₁ and R₂ (R₁ is series resistor, R₂ is shunt resistor) such that all ports are matched to Z₀ are:

R₂=NxZ₀/(N-1) (solve this resistor first!)

R1=Z₀x(NxZ₀+R₂(N-1))/(Z₀+R₂)

Here's the values for R₁ and R₂ for N-way splitters in 50 ohm system. We also show the "coupling factor", which is the ratio of arm output to splitter input power (we'll post that equation later).

For N=2, R₁=66.7, R₂=100, CF=-9.54 dB

For N=3, R₁=120, R₂=75, CF=-13.98 dB

For N=4, R₁=171.4, R₂=66.6, CF=-16.08 dB

For N=5, R₁=222.2, R₂=62.5, CF=-19.08 dB

For N=6, R₁=272.7, R₂=60, CF=-20.82 dB

Yes, it is possible to create an N-way Owen splitter with output arms set to different coupling values. Rather than trying to solve for the resistor values algebraically, we recommend you use an optimizer to do this job for you.

More to come!