# Impedance Matching Using a Proprietary Spreadsheet.



In this article we’ll discuss how to use this unique proprietary program to do impedance matching for any types of impedance without having much knowledge of Smith chart or impedance matching theories.

You only need to provide those basic data such as operation frequency, characteristic impedance, and to-be-matched impedance, and you’ll get the answers within a fraction of second.

We’ll explain step-by-step all details below.

However, if you would like to learn much more about impedance matching then these articles are great help:

Smith Charts-Basics, Parameters, Equations, and Plots.

Understanding Smith Chart by Learning Examples and Questions.

RF Circuits Impedance Matching Basics.

Impedance Matching-Using Lump Elements, Formulas, and Conversions-Part I.

Impedance Matching-Using Lump Elements, Formulas, and Conversions-Part II.

Impedance Matching by Using Smith Chart – A Step-by-Step Guide, Part I.

Impedance Matching by Using Smith Chart – A Step-by-Step Guide, Part II.

Impedance Matching by Using Smith Chart Associated with A Proprietary Spreadsheet, Part I-The Start Sheet.

Impedance Matching by Using Smith Chart Associated with A Proprietary Spreadsheet, Part II-The Results.

###### Understanding those parameters

$$Z=R+jX$$, to-be-matched impedance, $$R$$ is resistance, the real part and $$X$$ is reactance, the imaginary part.

$$Z_0$$, characteristic impedance, typically is 50Ω for RF.

$$z=Z/{Z_0}=r+jx$$, normalized impedance, $$r$$ is resistance, the real part, and $$x$$ is reactance, the imaginary part.

$$Y=1/Z=G+jB$$, admittance, $$G$$ is conductance, the real part and $$B$$ is susceptance, the imaginary part.

$$Y_0=1/{Z_0}$$, characteristic admittance, typically is $$1/50=0.02 siemens$$ for RF.

$$y=Y/{Y_0}=g+jb$$, normalized admittance, $$g$$ conductance, is the real part, and $$b$$ susceptance, is the imaginary part.

$$F$$, operation frequency in MHz.

$$|S_{11}| \le 1$$, return loss amplitude.

$$\angle S_{11}$$, return loss angle, it’s between 0° and 360°, or between -180° and 180°.

$$Γ=Γ_r+jΓ_i$$, reflection coefficient.

…….$$Γ_r=S_{11x}=|S_{11}|\cos \angle S_{11}$$.

…….$$Γ_i=S_{11y}=|S_{11}|\sin \angle S_{11}$$.

$$C_p (pF)$$, capacitor in shunt, unit pF.

$$L_p (nH)$$, inductor in shunt, unit nH.

$$C_s (pF)$$, capacitor in series, unit pF.

$$L_s (nH)$$, inductor in series, unit nH.

###### 4 Types of impedance to-be-matched

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 to 50Ω (or any other values) by using only 2 lumped elements, inductors and capacitors, if not considering the limited component values we are able to get as well as their tolerances.

You only need to provide the input data to get the answers you look for without getting involving in any calculation or manipulation. We’ve discussed in details how many alternative methods you can provide the data in this article,

Impedance Matching by Using Smith Chart Associated with A Proprietary Spreadsheet, Part I-The Start Sheet.

In addition to providing the information of $$Z_0$$ and $$F$$, you also need to provide the to-be-matched impedance using one of the 4 alternative methods.

Let’s briefly explain these 4 methods again: Fig. 2   Data entry area

Method #1, you provide $$S_{11}$$ ($$|S_{11}|$$ and $$∠S_{11}$$) in items #3 and #4. $$Γ$$, $$z$$, and $$y$$ will be calculated automatically. This is the most popular method as you very likely get $$S_{11}$$ from the datasheets.

Method #2, you provide $$Γ=Γ_r+jΓ_i$$ directly in items #5 and #6 to override the formulas. $$z$$ and $$y$$ will be calculated automatically.

Method #3, you provide $$z=r+jx$$ directly in items #7 and #8 to override the formulas. $$y$$ will be calculated automatically.

Method #4, you provide $$Z=R+jX$$ directly in items #11 and #12 to override the formulas, and copy $$r(a)$$ and $$x(a)$$ into $$r$$ and $$x$$. $$y$$ will be calculated automatically.

Unless you provide data via Method #1, using all 3 other methods would disturb the format of the “Data entry row”, and you should reset it to the normal situation to get ready for the next task by copying the “Backup row” as soon as you complete the current task.

It’s a good practice to always reset this “Data entry” row whenever you start a new project. Fig. 3   Reset “Data entry row”

###### Results you are looking for

There are four types of impedance that require slightly different matching circuits.

You’ll find the answers from one of the possible output boxes depending on $$z$$ and $$y$$ you’ve provided using one of those 4 methods. We’ll go through each type of impedance one-by-one below:

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

You should only check the Type #1 block and ignore all others.  Fig. 4   Type #1 impedance matching

In the figure 4, “Data entry” row shows that $$r=1.353 ≥ 1$$, so it’s a Type #1 impedance.

The 2 matching options are showed in the Type #1 block and we can read all matching components immediately.

Option #1: $$C_p (pF)=0.83$$ and $$L_s (nH)=2.14$$

Option #2: $$L_p (nH)=12.78$$ and $$C_s (pF)=1.41$$

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

You should only check the Type #2 block and ignore all others.  Fig. 5   Type #2 impedance matching

In the figure 5, “Data entry” row shows that $$g=1.353 ≥ 1$$, so it’s a Type #2 impedance.

The 2 matching options are showed in the Type #2 block and we can read all matching components immediately.

Option #1: $$C_s (pF)=5.11$$ and $$L_p (nH)=3.52$$

Option #2: $$L_s (nH)=2.07$$ and $$C_p (pF)=0.86$$

Type #3 impedance, r & g < 1, x > 0

You should only check the Type #3 block and ignore all others.  Fig. 6   Type #3 impedance matching

In the figure 6, “Data entry” row shows that $$r=0.309 < 1$$, $$g=0.591 < 1$$, and $$x=0.654 > 0$$, so it’s a Type #3 impedance.

The 4 matching options are showed in the Type #3 block and we can read all matching components immediately.

Option #1: $$C_p (pF)=0.83$$ and $$C_s (pF)=1.32$$

Option #2: $$C_p (pF)=1.91$$ and $$L_s (nH)=2.28$$

Option #3: $$C_s (pF)=5.71$$ and $$C_p (pF)=1.64$$

Option #4: $$C_s (pF)=0.98$$ and $$L_p (nH)=1.84$$

Type #4 impedance, r & g < 1, x < 0

You should only check the Type #4 block and ignore all others.  Fig. 7   Type #4 impedance matching

In the figure 7, “Data entry” row shows that $$r=0.350 < 1$$, $$g=0.483 < 1$$, and $$x=-0.777 < 0$$, so it’s a Type #4 impedance.

The 4 matching options are showed in the Type #4 block and we can read all matching components immediately.

Option #1: $$L_p (nH)=1.75$$ and $$C_s (pF)=1.06$$

Option #2: $$L_p (nH)=4.81$$ and $$L_s (nH)=2.84$$

Option #3: $$L_s (nH)=3.44$$ and $$C_p (pF)=1.49$$

Option #4: $$L_s (nH)=0.82$$ and $$L_p (nH)=2.02$$

Question #1: Operation frequency 1250 MHz, $$Z_0=50Ω$$, $$|S_{11}|=0.45$$ and $$\angle S_{11}=125$$, find all possible matching circuits.

Ans.  $$g=1.162 > 1$$, so this is a Type #2 impedance and there are 2 matching options.  Fig. 8   Type #2 impedance matching with 2 options

Question #2: Operation frequency 2300 MHz, $$Z_0=50Ω$$, $$Z=R+jX=38-j40$$, find all possible matching circuits.

Ans.  $$r=0.76 < 1$$, $$g=0.624 < 1$$, $$x=-0.8 < 0$$, so this is a Type #4 impedance and there are 4 matching options.

###### Fig. 9   Type #4 impedance matching with 4 options

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If you feel you totally understand the power of this program, then download it Here. ‘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.’ 