• An online smith chart tool to create matching networks. Smith Chart Tool. 0.2 0.5 1.0 2.0 4.0 10.0 Config. Characteristic Impedance (Z 0.
• The Smith Chart was originally created many years ago as an RF engineering aid by Phillip Smith of RCA. Actually, Smith may not have been the first inventor of this tool - a Japanese engineer named Kurakawa independently created a similar chart about a year before Smith.
• The Smith Chart Utility provides full Smith Chart capabilities, synthesis of matching networks, enabling impedance matching and plotting of constant Gain/Q/VSWR/Noise circles. The Smith Chart Utility is accessed from the Schematic window Tools or DesignGuide menus. The Smith Chart Utility documentation includes these sections.
• .The Smith Chart is a highly useful tool: –Complex Impedance Transformations –Determining VSWR, RL, and much more –Transmission Line impedance transformations.

The Smith Chart is a fantastic tool for visualizing the impedance of a transmission line and antenna system as a function of frequency. Smith Charts can be used to increase understanding of transmission lines and how they behave from an impedance viewpoint. Smith Charts are also extremely helpful for impedance matching, as we will see.

We have learned the impedance matching for all 4 Types of impedance using formulas & their conversions, and it’s recommended to visit these 2 articles before you continue to read further here:

In this article you’ll learn the step-by-step guide to match Type #1 and Type #2 impedance by simply using Smith chart without knowing those formulas. The only thing you need to do is enter S11 or to-be-matched impedance and you’ll get the approximate result by following all steps.

However, if you are vague to the Smith chart then you should STOP here and go back to learn the Smith Chart Basics first. Only after finishing reading the sequence and knowing all basics, you then can use this skill effectively.

Based on the values of r, g, x, and b, we can roughly categorize the impedance into 4 different types:

• Type #1: r ≥ 1, x any value.
• Type #2: g ≥ 1, b any value.
• Type #3: r < 1, g < 1, x > 0 or b < 0.
• Type #4: r < 1, g < 1, x < 0 or b > 0.

Fig. 1 Four types of impedance in the Smith chart .

Theoretically all these 4 types of impedance can be perfectly matched into 50Ω by using only 2 lumped elements, inductors and capacitors, if not considering the limited amount of component values we are able to get as well as their tolerances.

However, I would not suggest to use lumped elements for impedance matching over 5 GHz because it’s hard to find small enough elements, value and size, and the path length will play a main role for the matching process.

The very basic RULES of impedance matching are:

1. Add a lossless element, capacitor or inductor, to get the real part of either impedance or admittance to be 1.
2. Add the second lossless element to tune out the remaining imaginary part, reactance or susceptance, so the resultant impedance or admittance is a real number 1 ((z=1+j0) or (y=1+j0)).

Matching Type #1 impedance: r ≥ 1, x any value.

Type #1 impedance is located within the area of (r=1) circle.

The process to match a Type #1 impedance into 50Ω:

1. If return loss (S_{11}) or reflection coefficient (Γ) is given by datasheets, then refer to this article Smith Charts-Basics, Parameters, Equations, and Plots to learn how to convert the number to impedance.

2. Normalize the given impedance. If the impedance is (Z=R+jX), then the normalized impedance is (z=Z/50=r+jx).

Fig. 2 Normalize the impedance

3. Locate the impedance (z=r+jx) in the Smith chart, point X.

Fig. 3 Type #1 impedance in the Smith chart

As showed in Fig. 3, we can simultaneously read the impedance (z) and admittance (y) of point X:

(z=r+jx=2.0+j1.0)

(y=g+jb=0.4-j0.2)

Fig. 4 Type #1 impedance (z) & (y)

Follow the first basic rule of impedance matching, add a lossless element, capacitor or inductor, to get the real part of either impedance or admittance to be 1.

The only options to satisfy this first rule is add a capacitor, Option #1, or an inductor, Option #2, in shunt to move the admittance (y) along the (g=0.4) circle until meeting (r=1) circle at points O1-S1 & O2-S1.

Fig. 5 Type #1 impedance matching, Step 1

We can fairly accurately read the locations of both points in the Smith chart:

Point O1-S1:

(z=r+jx=1-j1.22)

(y=g+jb=0.4+j0.49)

The admittance of the added capacitor (C_p) is (0.49-(-0.2)=0.69)

Point O2-S1:

(z=r+jx=1+j1.22)

(y=g+jb=0.4-j0.49)

The admittance of the added inductor (L_p) is (-0.49-(-0.2)=-0.29)

We then follow the 2nd rule and move both points O1-S1 & O2-S1 along the (r=1) circle to the origin (z=1) by simply adding an inductor, Option #1, or a capacitor, Option #2, in series respectively.

Fig. 6 Type #1 impedance matching, Step 1 & Step 2

And the impedance values of added elements are:

Option #1: (L_s=0-(-1.22)=1.22)

Option #2: (C_s=0-1.22=-1.22)

Question: Match this Type #1 impedance (z=1.4-j0.6) using Smith chart.

Ans.

Option #1: (C_p=0.23) (L_s=0.81)

Option #2: (L_p=-0.75) (C_s=-0.81)

<<<<<<<<<<>>>>>>>>>>

Matching Type #2 impedance: g ≥ 1, b any value.

Type #2 impedance is located within the area of (g=1) circle.

The process to match a Type #2 impedance into 50Ω:

1. If return loss (S_{11}) or reflection coefficient (Γ) is given by datasheets, then refer to this article Smith Charts-Basics, Parameters, Equations, and Plots to learn how to convert the number to impedance.

2. Normalize the given impedance. If the impedance is (Z=R+jX), then the normalized impedance is (z=Z/50=r+jx).

Fig. 7 Normalize the impedance

3. Locate the impedance (z=r+jx) in the Smith chart, point X.

Fig. 8 Type #2 impedance in the Smith chart

As showed in Fig. 8, we can simultaneously read the impedance (z) and admittance (y) of point X:

(z=r+jx=0.4-j0.2)

(y=g+jb=2.0+j1.0)

Fig. 9 Type #2 impedance (z) & (y)

Follow the first basic rule of impedance matching, add a lossless element, capacitor or inductor, to get the real part of either impedance or admittance to be 1.

The only options to satisfy this first rule is add a capacitor, Option #1, or an inductor, Option #2, in series to move the impedance (z) along the (r=0.4) circle until meeting (g=1) circle at points O1-S1 & O2-S1.

Fig. 10 Type #2 impedance matching, Step 1

We can fairly accurately read the locations of both points in the Smith chart:

Point O1-S1:

(z=r+jx=0.4-j0.49)

(y=g+jb=1.0+j1.22)

The impedance of the added capacitor (C_s) is (-0.49-(-0.2)=-0.29)

Point O2-S1:

(z=r+jx=0.4+j0.49)

(y=g+jb=1.0-j1.22)

The impedance of the added inductor (L_s) is (0.49-(-0.2)=0.69)

We then follow the 2nd rule and move both points O1-S1 & O2-S1 along the (g=1) circle to the origin (z=1) by simply adding an inductor, Option #1, or a capacitor, Option #2, in shunt respectively.

Fig. 11 Type #2 impedance matching, Step 1 & Step 2

And the admittance values of added elements are:

Option #1: (L_p=0-1.22=-1.22)

Option #2: (C_p=0-(-1.22)=1.22)

Question: Match this Type #2 impedance (z=0.5+j0.3) using Smith chart.

Ans.

Option #1: (C_s=-0.8) (L_p=-1.0)

Option #2: (L_s=0.2) (C_p=1.0)

We’ll continue to discuss Type #3 and Type #4 impedance matching in the next article.

‘Note: This is an article written by an RF engineer who has worked in this field for over 40 years. Visit ABOUT to see what you can learn from this blog.’

This page describes the free Smith Chart impedance matching program from Iowa Hills Software.

See this page for a set of useful matching circuit equations.

Smith Charts allow the user to design impedance matching circuits. This is done by entering a load impedance on the chart, then altering that impedance with series and shunt components. This program allows for the following components to be used.

You may choose to work with ideal components (no parasitics or loss), or you may specify the Q and parasitic reactance associated with your components. It is quite interesting to see the effects of the parasitics, even for the simplest of circuits. It is also nice to be able to adjust a component value after it has been placed. This can be done by selecting the text cell below the schematic symbol and using the arrow keys to modify the value.

The program was written for practical use. As such, the user must specify the tolerance for the capacitors and inductors which in turn specifies the discrete values used by the program. For example, if specifying 10% inductors, then the allowed inductor values go as 1.8, 2.2, 2.7, etc. You cannot place a 2.45673 nH inductor for example. The effect of using these discrete values is shown with the short changing color segments. For example, a segment drawn as green, dark green, green, dark green, etc. would represent 1.8, 2.2, 2.7, 3.3 etc. This gives the user a good sense of circuit's sensitivity.

The program can also plot S parameter data, along with their stability circles and the stability factor k. The user may match to S11 or S22 directly, or choose to match to the optimal bilateral matching impedance (if k >= 1).

An FAQ
A frequently asked question when getting started with the Smith Chart is: To match Z to 50 Ohms, do I start on the Smith Chart at Z, or Z conjugate?

We start at Z, but a simple example shows an important aspect about these matches. Here we match a load of 75 - j100 to 50 Ohms at 1 GHz. Then on the right, we work through the problem in reverse to end up at the conjugate of our load.

This simple example shows a fundamental fact about circuits. If a circuit is designed for maximum power transfer, then you can break the circuit at any point and looking to the left you will see Z, and to the right you will see Z conjugate. If this isn't the case, maximum power transfer isn't occurring.

Q Circles

The program allows for Constant Q and VSWR circles to be plotted on the chart. Q circles are used as a way to control the bandwidth of the match. The following example should make the point.

In the plots below we show two ways to match a load of 118 - j99.5 to 50 Ohms. In the first example, we draw a Q=1 circle on the Smith Chart. We then choose a circuit topology and component values that keeps the impedance traces within the Q Circle. Then we use a Q=6 circle, and do the same thing. Notice the effect on the bandwidth of the match.

It should ne noted that in general, these matching circuits are seldom this easy. It is more typically the case that the load being matched to is much further out on the Smith Chart. In other words, the Q of the load is high. In those situations, the bandwidth of the match is controlled by the load, not the matching circuit. The only way to improve the Q of the match (widen its bandwidth) is to add either shunt or series resistance to the match, which of course introduces losses.

It is worth noting that a transformer traces out the same path on the Smith Chart as a Q Circle. VSWR circles can also be plotted on the chart, but they have little practical value in the design of a matching network.

Q=1 Match

Q=6 Match This match uses values that push the impedance traces out to Q= 6. Note the narrower bandwidth of this match as shown by the return loss plot.

Q circles show a fundamental fact about matching. It is usually the case that the engineer needs a broadband match, but to have a broadband match, we must stay within a low Q circle. Notice that if the load you are matching to is purely resistive, then it is possible to stay within an arbitrarily low Q circle, but you may need to use a large number of components to get back to 50 Ohms.

On the other hand, if the load is highly reactive, 2 + j50 for example, then the load has a Q of 25, and it is impossible to do a lossless broadband match, no matter how many components you use.

Bilateral Matching

To start, let us make three points about this subject that need to be understood.

1. Bilateral matching is done with 2 port s parameter data. This is typically done when designing the input and output matching circuits for a high frequency transistor. The transistor manufacturer typically supplies the s parameter data.

2. Bilateral matching is only used for devices with |S12| > 0. This is generally the case. The only 2 port devices with S12 = 0 are ideal isolators.

3. If S12 = 0, then there is no path from port 2 to port 1, and the bilateral match reduces to a conjugate match. Or said a bit differently, if S12 for your device is very small, then bilateral matching isn't required and a simple conjugate match will suffice.

The basic idea for bilateral matching is fairly simple. If S12 ≠ 0, then there is a signal path from the output back to the input. The effect of this is that the device's input impedance is affected by the load, and the device's output impedance is affected by what is connected to it's input. Consequently, the only way to match such a device is to calculate the input and output matches simultaneously. We do this by using the device's s parameter data and the equations that follow.

The following is a screen shot from a MathCAD file. The equations were taken from High Frequency Amplifiers by Ralph S Carson, Wiley and Sons, 1982. The final results are the variables Z1opt and Z2opt. These two variables can be a bit confusing. i.e. Are we calculating the impedance of the device, or the impedance the device wants to see.

There is less confusion if one remembers that the outcome of these equations will yield a result fairly close to a simple conjugate match. So it helps to note their value relative the Z1 and Z2 as calculated from S11 and S22. The conjugate of Z1opt and Z2opt are relatively close Z1 and Z2. Thus, the conjugate of Z1opt and Z2opt represent the optimal impedance of the device itself.

Consequently, if using a Smith Chart to calculate a matching network, start at the conjugate of Z1opt and Z2opt (start at the device, as always), and work toward 50 Ohms.

The Iowa Hills Smith Chart program will do these calculations. The user simply needs to read in an s parameter file, and specify the match frequency.

Antenna Matching

Many people want to use a Smith Chart to design an input match to an antenna. Be warned however, this probably will not work.

If you use a network analyzer to measure an antenna's input impedance, you will notice that S11 can be made to move all over the place by moving an object around the antenna. This is a very good sign as it means that the antenna is well coupled to the atmosphere and any changes in the antennas surroundings, which also changes the amount of signal reflected back to the antenna, appear as a change in S11. Only very poor antennas are insensitive to their surroundings.

It has been my experience that good antennas are also very sensitive to their source impedance. Which is to say, a change in the source impedance also changes the impedance of the antenna. (Emphasis on the word 'experience' here, I have no theory to back this statement.) The result of this is; there is not a good way to calculate a matching circuit for antennas.

Smith Chart Basics

It is certainly the case that some low frequency antennas use matching circuits, because they don't have a choice. To the best of my knowledge however, these circuits are either hand tuned, or tuned programmatically in the field, to minimize the reflected power.

An antenna is supposed to be the impedance matching circuit between 50 Ohms and 377 Ohms. If the antenna isn't presenting 50 Ohms to you, the problem should be fixed by modifying the antenna. A way to think about this is; if an antenna looks reactive, it is by definition storing energy, and this is the last thing you want an antenna to do as it will inevitably lead to losses. Low loss antennas look purely resistive.

Smith Charter

In general, using an impedance matching circuit to fix an antenna's input impedance is a poor approach to take. The final result will likely be a very lossy antenna. Of course, in some situations, you don't have a choice in the matter.

Miscellaneous Tools

A pad calculator, units converter, and free-space path loss calculator are built into the program, because it was easy to do and they are handy to have in the lab. Experienced engineers probably have the units and path loss conversions memorized, but the pad calculator is less trivial.

Smith Chart Reflection Coefficient

Calculating the resistor values for a pad isn't particularly difficult, but there are limitations the RF engineer must pay attention to if the load and source are to remain matched. The screen shot below illustrates this point.

Smith Chart Impedance Matching

In this example, we want a 3 dB pad between a 50 Ohm Source and a 75 Ohm load. As the program shows however, the minimum attenuation for this configuration is 4.0 dB if both the source and load are to remain matched. If we are willing to allow either the source or the load to be unmatched, then we can use an L pad as shown here.

This Smith Chart program is free, and available on the Download Page.

Smith Chart Solver

RF = ReFined

Smith Chart Impedance Matching

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