From the figure the frequency was 5 Ghz. The schematic of this design is shown below:

Note that the impedance of the line is: sqrt(50*100). The length of the line is a quarter wavelength ( 1 wavelength = 60 mm at 5 Ghz).

For more information on impedance matching please refer to the available book : “VSWR and Impedance matching techniques”, available from Amazon,

In addition a forthcoming book that includes many other techniques and scripts is in preparation.

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A low noise amplifier module with NF = 1 dB across the 100 Mhz to 3.0 Ghz band with typical 17.7 dB small signal gain over the band.

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Coupling port power 20 dB, Directivity 12 dB. Main line loss between 370 Mhz and 470 Mhz is 0.25 dB max. Characteristic impedance is 50 Ohm

Ports are :

1 – the input port

4 – output port

6 – coupled port in the forward direction

3 – coupled port in the reverse direction

Now to further our analysis lets connect a load to port 1 and drive port 4. So this is a reverse direction operation for this coupler.

To use some numbers, lets input 0 dBm at port 4. Then since the loss on the mainline is 0.25 dB the power arriving at port 1 is -0.25 dBm. Also:

lets assume the load is exactly 50 Ohm and we terminate port 3 with also 50 Ohm. Now the power coming out of port 6 is -32 dBm if the coupler is ideal. (directivity + coupling ).

Now lets assume that the load is no longer 50 Ohm but 100 Ohm. Now there will be reflected power also being added to the power out of port 6. The difference between the

– 32 dBm and the total power being measured at port 6 with 100 Ohms is the reflected power PR.

Then the return loss is simply

RL=10log10(PT/PR) dB.

Here PT is 0 dBm. Once RL is known other parameters can be calculated.

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D = s31 + s21 – s32. where s31=coupling ratio, s21=insertion loss and s32 = isolation. All these are defined negatively in dB, but D itself is stated positively. A shorter form is also used for forward measurements as D = s31 – s32. The question is: why is directivity important?

To elaborate a little: power is applied to port 1 and output at port 2. Some of the applied power is coupled to port 3 with a coupling factor of K^2. At port 3 part of the input power is sampled. Port 3 is the coupling port. Port 4 is the isolation port where ideally, no input power should appear. Any of the ports can be defined as the input port provided the other ports are appropriately labeled.

Mathematically speaking we can define: Coupling = 10Log(P1/P3) = -20LogK ( dB). Also in a similar fashion the other parameters can be defined: Directivity = 10Log(P3/P4) = + 20Log[K/ABS(s14)]. Isolation = I = 10Log(P1/P4) = -20Log[ABS(s14)] dB. Insertion loss = L = 10Log(P1/P2) = -20Log[ABS(s12)] dB.

The coupling shows how much of the input power is coupled to port 3. The directivity shows how well the coupler isolates forward and reverse signals. Isolation shows how much of power is delivered to the isolated port. The insertion loss provides the calculation for the amount of power delivered to the output port, less the power delivered to the coupled and isolated ports. In an ideal coupler the directivity and isolation are infinitely high.

Using the example of measuring an unknown impedance with a signal source, a detector and a coupler, we see that if the unknown impedance is perfectly matched to the source impedance then there is no reflection of power at all, and there is no reverse wave. So in this case we will measure the impedance perfectly. Its simple enough ! However, if the unknown impedance is not matched to the source impedance then there will be a reflected wave. We sample this using port 4. In this case however, the coupler not being ideal will transmit part of the reverse signal to port 3, the coupling port that we also use to sample the forward signal. Now there will be an error in the measurement. We need as little of the reverse signal in the coupling port as possible. A characteristic of the coupler. This is why directivity is important. The higher the directivity the less error we will get. A very good article on this topic is provided by REF1: ” Directivity and VSWR measurements”, by Doug Jorgesen and Christopher Marki of Marki Microwave Inc. They also provide curves of error versus directivity etc. A very readable article. Please visit our website for more articles of interest, calculators and a description of what we do and some of our products.

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The figure above is the D.S current in mA.

The figure below is the simulated power gain and PAE.

We hope these will be of help to aspiring designers of Class F amplifiers. Please visit the Signal Processing Group Inc., website for more information and articles of interest.

]]>In double stub matching the two stubs are spaced a predetermined distance away from each other. These distances are typically λ/8, λ/4, 3λ/8, 5λ/8 etc. Knowing what we know about a length of line acting as a transformer, we know that the length of line between the two stubs acts as a transformer. The action of this transformer is to convert the admittance at the position of stub 2 to a different admittance at the position of stub 1. So we start from the position of stub 2.

In order that stub 2 can be finally used to match the line admittance, the real part of the admittance at the position of stub 2, on the line, has to be 1.0 (normalized value). Its susceptance is then jB. jB is the susceptance that is cancelled using stub 2 to ultimately get the matching to the line admittance. The admittance at the position of stub 2, (without the stub) lies on the constant conductance, g = 1 circle. The admittances on the g = 1 circle are all the possible admittances at the stub 2 position for a match to take place.

To reiterate, as a result of these deliberations, that some point of the VSWR circle formed by the position of stub 2, must intersect the g=1 or the unity conductance circle on the Smith Chart.

We also conclude, that the admittance at the position of the first stub, must lie on

a circle of equal radius but having its center rotated (moved to or displaced) by the spacing between the stubs towards the load. Lets call this spacing ‘d’.

This circle is called the spacing circle.

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