LNA Design Tutorial Series 8

LNA Design Tutorial Series 8 - Wilkinson Splitter

Low Noise Microwave Amplifier Design Tutorial - Part 8 Wilkinson Divider Today you can find here the Wilkinson power divider design that will be used in the balanced microwave amplifiers used in this LNA design tutorial. The original analysis had made use of Anaren's XingerIII quadrature hybrid couplers. These would certainly do the job well. But to keep costs low, a printed microstrip design has been chosen. The 90 degrees of phase offset will be achieved using a quarter lambda of 50 ohm transmission line as shown below. The image below is an example of how this is implemented in practice.

Balanced Microwave Amplifier using Wilkinson Dividers

To remain up to date with projects I am pursuing, I encourage you to sign up to my mailing list. Subscribe

Impedance Transformation In order to minimize Standing Waves when dividing the RF signal path, there are multiple approaches you can choose from. A number of those solutions employ what is known as theQuarter Wave or Quarter Lambda impedance transform.

A special condition occurs when the length of a transmission line is one quarter of the wavelength for a given frequency as shown in the formulas below. In the following equations, Zo is the impedance of the line that will transform from Zin to ZL.

When Length = 1/4 Wave or 90 degrees then: Zin/Zo = Zo/ZL Zin = Zo^2/ZL and Finally Zo = (Zin*ZL)^0.5 The resulting formula computes the impedance of the 90 degree length of line required to transform from Zin to ZL. Examine the smith chart image below and you will see how it works.

Quarter Wave Impedance Transform on the Smith Chart

Wilkinson Divider In the case of the Wilkinson power divider the equal splitting of the transmission line into two paths requires an impedance transform to maintain the characteristic impedance at all three ports. As

you've just learned, we will require both Zin and Zout variables defined so you can calculate Zo. In a 2 way Wilkinson Divider, the "Isolation Resistor" should be equal to 2*Zin and will represent the Zout variable in terms of impedance transformation. In this case Zin = 50 ohms giving you an Isolation resistor value of 100 ohms and a ZL of 100 ohms. Lets see how these numbers work in the formula previously discussed. R in this case is ZL. Zo

=

(50*100)^0.5

=

70.7

ohms.

In the case of the Wilkinson Divider you can use a simpler formula but knowledge of theQuarter Wave Impedance Transform is something that can serve you well when the need arrives. 

Zo=Zin*2^0.5

Wilkinson power divider

Wilkinson Power Divider at 1880MHz

Artwork for the 90 degree phase offset Power Divider

When designing a circuit that is depending on the electrical length of the transmission line such as the Wilkinson Power Divider does, you will want to take the time to read the help files for the micro-strip Bend or Curve models you choose in your simulation software. Depending on which tool and model you select, the model may be doing a simple straight transmission line approximation and apply an electrical delay for the equivalent length of the bend. This will cause significant errors in your result. If you are in doubt, use a 2.5 or 3 Dimensional Electromagnetic Simulator to model your bends. Alternatively, you can find Bend models that use EM Mode-Matching which just as good as a 2.5 or 3 Dimension Simulation in most cases but faster.

One tip you want to remember is that the more bends you use, the shorter the line will need to be to achieve the 90 degrees of phase shift. This is due to the inevitable shunt capacitance generated by these bends that cause your transmission line to attain j0 ohms prematurely. In this case you may need to revisit your line widths to ensure the matching is not adversely affected. Complete Design Schematic of the Wilkinson Power Divider Below is the complete schematic of the Wilkinson Power Divider Design.

Schematic for the Wilkinson Power Divider and 90 degree phase delay Circuit

S-Parameter Results of the Simulated Wilkinson Power Divider

PASS!!

90 Degree phase difference between output ports 2 and 3. Phase Difference = (360 Deg - 123.8 Deg) - 147.1 Deg = 89.1 Deg PASS!! Conclusion This Wilkinson Power Divider and 90 degrees of phase offset is an effective substitute for the Quadrature Hybrid Coupler in narrow band applications. In the next installment of the LNA Design Tutorial Series you will be guided through the

implementation described here.

of

the

evaluation

circuit

To remain up to date with projects I am pursuing, I encourage you to sign up to my mailing list. Subscribe