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13.6. Impedance Matching Wizard (iMatch)

The Impedance Matching Wizard (iMatch) uses the iFilter Filter Wizard interface. Starting, running, and closing the iMatch Wizard are similar to the same operations with the iFilter Wizard. For detailed information, see “iFilter Filter Wizard”.

This wizard displays in the NI AWR Design Environment suite if you have the proper license file (FIL-350, FIL-300, or FIL-050) to run the wizard.

13.6.1. Using the iMatch Wizard

iMatch can run as a stand-alone license or as an integrated feature with an iFilter license. In a stand-alone configuration, the iFilter Wizard can only design impedance matching type circuits. In an integrated configuration, the iFilter Wizard recognizes iMatch circuits as a special filter type.

13.6.1.1. Running the iMatch Wizard

You can run the iMatch Wizard to create a new impedance matching network or to modify an existing impedance matching network. To create a new matching network, open the Wizards node in the Project Browser and double-click the iFilter Filter Wizard then click Matching.

You can edit terminations, specifications and matching options. After every change, the wizard recalculates the values, redoes the realization (layout or part selection) and calculates and plots the response. You do not need to press a special button after modifications as all the views are kept current.

To enter a different value or specification in the Matching dialog box you can use the keyboard, click the up/down arrows next to an option to increase/decrease values, or use the mouse wheel (click in the desired edit box and scroll the mouse to increase/decrease the value). The step size is automatic based on the type and value of the edit box. Press Ctrl while scrolling to increment/decrement with a smaller step size.

13.6.1.2. Closing the Wizard

To close the iMatch wizard:

  • Click OK in the Matching dialog box to save your design.

  • In the main iFilter dialog box, click Generate Design to create a schematic, graph(s) and other items in the NI AWR Design Environment suite.

  • Click OK to create a filter design item under the iFilter Filter Wizard node in the Project Browser only. No schematic, graph(s) or other items are created. This is the only way to save a wizard state for later reuse.

  • Click Cancel to close the Matching dialog box without saving.

13.6.2. iMatch Wizard Basics

The Matching dialog box (main iMatch dialog box) as shown in the following figure, is comprised of specifications on the left-hand side and graphics on the right-hand side. Graphics include the insertion loss and return loss graph, Smith Chart, and schematic/layout drawing.

To create a typical iMatch design:

  1. Click the Edit Terminations button to specify load and source terminations in the Matching Terminations dialog box, then click OK.

  2. To select additional options, click the Matching Options button to display the Matching Options dialog box.

  3. In Fo, enter the center frequency of the matching network.

  4. Click one of the six buttons in the Matching group to select the matching type. See “Impedance Matching Types” for information on the matching types.

  5. Click the Matching Options button and select an option in the Matching Options dialog box.

  6. Select a Reactance Cancellation method for terminations. See “Reactance Cancellation” for more information on the available options.

  7. In Q, # seconds, and EL [deg], enter further design specifications if available.

  8. Repeat steps 3 - 7 to obtain the most appropriate design.

  9. Click OK to save the current design, close the dialog box and transfer the data to the main iFilter dialog box. You can make further adjustments such as specifying the Fo, or selecting technology parameters in this dialog box.

  10. Reopen the Matching dialog box as required from within the main iFilter dialog box.

  11. Click the Generate Design button in the main iFilter dialog box to generate the design (schematics, graphs, and data) in the Microwave Office Project Browser.

13.6.2.1. Matching Terminations Dialog Box

The Matching Terminations dialog box is used to specify source and load impedances (terminations) of the impedance matching design. To access this dialog box, click the Edit Terminations button in the Matching dialog box.

Specifications are grouped on the left side of the dialog box. Specifying terminations is identical for source and load. A termination can be represented by a single element, a combination of elements, or a frequency-impedance data array. Major passive elements (RES, IND, and CAP) and their various combinations are available for selection. After selecting a model for the termination, enter the R, L or C values if they are enabled based on your selections. On the right side of the dialog box, a representative schematic and selected frequency information are shown for reference. The following termination types are available in iMatch:

Some devices that require matching are represented by impedance vs. frequency. In this case, select Data from the (source) or (load) box and enter the data in the Freq, R, jX box. You can specify Data as frequency, real, and imaginary parts of impedance, with comma delimiters, for example:

100, 45, 5

150, 50, 7

200, 55, 9

This means 45+j5 Ω at 100MHz, 50+j7 Ω at 150MHz, and 55+j9 Ω at 200MHz. You can use the following means to enter data in the Freq, R, jX box:

  • Manually enter the data

  • Click the Load From File button to load data from a .S1P or .S2P Touchstone format file. If the file is .S1P format, then the impedance is given in the file. If the file is .S2P format, you can use either S11 or S22 as the matching impedance. This choice is presented in a simple dialog box: Use S11 for input impedance? Click NO to use S22. Click YES to use S11, NO to use S22 for the impedance.

  • Click the Load From Schematic button to load data dynamically from Microwave Office schematics. A Select Schematic and Port dialog box displays to allow you to select an Microwave Office schematic in the current project. The schematics list contains schematics with only 1 or 2 ports. Select Port 1 to use this port to calculate input impedance towards the matching network (the iMatch wizard calculates the input impedance starting from the first element after port 1 looking into port 2). Select Port 2 to look into port 1 as input impedance. Click OK to close the dialog box. The schematic is analyzed with an auto-selection of frequency range and input impedances are calculated.

If the methods are successful, the Freq,R,jX box is filled with data. Up to 101 rows of data are allowed, the rest are ignored. You can edit the data in the box at another time to trim excess or add more values.

On the right side of the dialog box, source and load impedances are calculated and displayed as Zin1 and Zin2 respectively. The real and imaginary parts are displayed separately. If the terminations are modeled as a combination of R,L,C values, these impedances are exact. If they are given in Freq,R,jX format, the impedances are interpolated at the frequency of interest.

Under Analysis, you can enter the minimum and maximum frequencies within which the impedances are calculated and displayed. Click the Auto Freq Range check box if you want the wizard to determine those frequencies.

13.6.2.2. Matching Options Dialog Box

The Matching Options dialog box currently contains only a lumped element display choice. For mixed element designs, you must use lumped elements along with transmission lines and/or stubs. Various size options exist for lumped elements. To use a specific element size, select the desired option in the group. If you select Automatic, iMatch decides the optimum size of elements based on technology selection and transmission lines widths and lengths in the design. Click OK to close the dialog box.

13.6.2.3. Analysis Frequency Range

To change the analysis frequency range quickly, click one of the following toolbar buttons in the middle of the dialog box:

From left to right, these buttons are:

  • Increase Analysis Span

  • Decrease Analysis Span

  • Narrow Analysis Span (center frequency Fo is assumed)

  • Wide Analysis Span (center frequency Fo is assumed)

  • Ultra Wide Analysis Span (center frequency Fo is assumed)

  • Auto Span when Passband Changes (moves the center frequency of the analysis range, along with changes in Fo)

13.6.2.4. Chart Setting Dialog Box

To manually enter the analysis frequency range, click the Edit Chart Settings button.

The Chart Settings dialog box displays to allow you to specify Frequency Range values.

13.6.2.5. Graphics Display Control Options

You can configure the graphics (schematic/layout) side of the dialog box to display schematic, layout, schematic info, or layout info using the following buttons.

This action is similar to that of the iFilter Wizard. See “Viewing the Schematic and Layout” for more information.

You can rotate the position of the items on the graphics side (schematic/layout, insertion loss-return loss graph and Smith Chart) for better display details by clicking the Change View Order of Drawing and Plots button. Note that the windows change places.

13.6.3. Impedance Matching Basics

Impedance matching circuits contain three sections: source termination, matching network, and load termination. This statement also implies a topology which can be shown as a cascaded element schematic, as shown in the following figure.

Conventionally, source and load terminations are shown on the left and right, respectively. In the previous schematic, Z1 (or ZS) is named as the source impedance, and Z2 (or ZL) is named as the load impedance. Zin2 is the input impedance of the load termination after being matched by the matching circuit. Likewise, Zin1 is the input impedance of the source termination after being matched by the matching circuit.

Termination and impedance are used interchangeably in the context of matching and filtering circuits, so source impedance and source termination mean the same thing.

13.6.4. Maximum Power Transfer

Impedance matching is the practice of designing circuits:

  • to minimize reflections between source and load terminations, and

  • to maximize power transfer from source to load.

Typically, matching circuits contain reactive elements and transmission lines (just like filters), that do not intentionally cause dissipation.

To maximize power transfer, the output impedance of the source termination must be equal to the complex conjugate of the input impedance of the load termination.

In the previous schematic, the following condition provides the maximum power transfer condition:

Z1 = Zin1*

so,

R1 + jX1 = (Rin1 + jX1)* = Rin1 - jXin1

To satisfy this equation,

Rin1 = R1, and

Xin1 = -X1

There are two ways to solve these equations and find a matching network. The first is to perform circuit synthesis by constructing transfer functions for complex terminations and extracting element values. Complex impedance circuit synthesis is cumbersome and very rarely performed in practical designs. The second method is to cancel reactances at the first chance and deal with purely resistive terminations. Many topologies are available with explicit formulations or iterations which can match resistive terminations over satisfactory bandwidths. In more than 95% of applications, the second method is adequate.

In iMatch, where appropriate, reactive terminations (source or load) are simply turned into resistive networks by applying the cancellation method you choose.

13.6.5. Reactance Cancellation

iMatch provides four reactance cancellation methods in the Matching dialog box Reactance Cancellation option. You can select different methods for source and load, as displayed. In the following method descriptions, only the load side is shown. The same methods are applicable to the source side if the source termination is reactive.

13.6.5.1. Lumped (Series) Cancellation Method

In this method, a series IND or CAP is placed next to the termination. If the reactive part of the termination is positive, a negative reactance is needed and a CAP is added. If the reactive part is negative, a positive reactance is needed and an IND is added.

The series element value is calculated from the required reactance and frequency of matching, as specified in the dialog box. For inductors, X = 2*π*Fo*L. For capacitors, X = 1/(2*π*Fo*C).

The input impedance seen from the far side of the matching element is now purely resistive and it is the same as the resistive part of the termination, for example, Zin = R’ = R

This method is very simple and effective except for in the following two instances:

  • When used in circuits where the series arm is also used for supplying DC currents, a capacitive cancellation is not adequate because a series capacitor is a DC-block.

  • Rin is the same as R after cancellation. When R is too small or too large, this may pose a matching problem for intended bandwidths. It may be better to use the shunt cancellation method for extreme values of R.

13.6.5.2. Lumped (Shunt) Cancellation Method

In this method, a shunt IND or CAP is placed next to the termination. If the reactive part of termination is positive, a negative reactance is needed and a CAP is added. If the reactive part of a termination is negative, a positive reactance is needed and an IND is added.

The shunt element value is calculated from the required reactance and frequency of matching, as specified in the dialog box. The required reactance is calculated from Xm = -(R*R+X*X)/X.

The input impedance seen from the far side of the matching element is now purely resistive and calculated from

Zin = R’ = Xm*Xm*R / (R*R + (Xm+X)*(Xm+X)).

This suggests that the resistive part of input impedance (or simply the input impedance) is no longer equal to R. This offers a big advantage for terminations that have extreme resistive parts. The shunt Reactance Cancellation might bring it to reasonable levels. For example, for Z = 1 + j5 Ω, when a shunt -5.2 Ω is added to this termination using a shunt capacitor, the input impedance becomes Zin = 26 Ω. Compared to 1 Ω, 26 Ω offers more matching options and wider bandwidth.

13.6.5.3. Stub (Shunt) Cancellation Method

This cancellation method is similar to the lumped (shunt) cancellation method, except the shunt element is an open circuit transmission line stub. Xm and the resultant R’ are calculated the same way. Xm, however, is used to find the length of the stub and the specified stub impedance. You specify stub impedance, Zo, in Reactance Cancellation as Line Imp [ohm].

For negative Xm values, the line length is EL = -Zo/Xm. For positive Xm values, 180-degrees is added to EL. Short-circuited stubs are not offered as a solution as they are not practical. In most cases, these circuits are used in matching amplifier inputs and outputs. Short-circuited stubs also short-circuit the gate bias or drain supply to ground, which is not desirable.

13.6.5.4. Transmission Line Cancellation Method

Transmission lines are very useful matching elements, as they can alter the input impedance in a number of ways.

The input impedance of a transmission line terminated by a load impedance ZL is given as:

By selecting a Zo and Theta, this sophisticated equation can be manipulated to give:

  • purely reactive input impedance

  • purely resistive input impedance

  • a certain VSWR level

In this cancellation method, you specify Zo in Reactance Cancellation as Line Imp [ohm]. Electrical line length is then calculated to obtain Zin = purely real impedance.

Reactance Cancellation is available in most reactive matching conditions, except for TL+Stub types. For TL+Stub matching types, an inherent transmission line cancellation is applied as part of the selected matching option.

13.6.5.5. Required Level of Matching

When the impedance matching is “perfect” at a frequency, the circuit has infinite return loss, and the transmission is ideal (lossless). This frequency is also called a “reflection zero” in filter terminology. A reflection zero is rarely achieved in practical circuits due to certain dissipative losses.

You do not need to obtain perfect matching; a level of return loss may be adequate for the application of interest. For example, a 10 to 15dB input return loss may be satisfactory for a power amplifier. The performance difference that is obtained by matching with 20dB return loss is not significant. Otherwise, obtaining a good output match is crucial, as the power of interest is typically 5-10dB higher compared to the input. For example, for a 50W amplifier with a 15dB match on input and output, a 5dB improvement in the match corresponds to 0.2W at the input and 2W at the output. Beyond a 20dB return loss, there is not much gain in terms of transmitted power.

13.6.5.6. Single Frequency Point Matching

Every matching section adds a reflection zero to the return loss, so it improves matching bandwidth. You can add reflection zeros across the bandwidth and obtain wide-band performance. The reflection zeros can also all be gathered at a single frequency to obtain a “deeper” return loss in the center (> 30dB) and shallower return loss at the band corners (10-15dB). The first method requires circuit synthesis with unequal and/or complex terminations. The second method is straightforward and it works well for practical applications. iMatch uses the “single frequency point method”, where the matching is performed at a single frequency. Up to 4th order matching circuits are available, which meets most bandwidth requirements even with extreme impedance ratios.

13.6.5.7. Step-by-step or iMatch

In many textbooks, step-by-step impedance matching is described where you can arbitrarily add elements to obtain impedance matching at a single frequency. This method teaches you the physical side of matching in terms of how specific elements contribute to the input impedance of a circuit. This method is worth learning, however there are two drawbacks associated with the step-by-step matching method. First, it takes time to test different matching types and choose the best one based on size, cost, and other variables. Second, it is hard to predict frequency performance, as the matching is only obtained at a single frequency. You can apply techniques such as staying in constant Q circles, but these techniques only give an approximate solution. You still must simulate the circuit in a circuit simulator to determine wideband performance.

In iMatch, you can perform step-by-step matching by clicking the Manual button under Matching. In manual mode, iMatch uses the manually selected elements and their values and does not perform any further matching. The response and layout (if there is one) are still calculated and drawn as expected.

Other than manual matching, iMatch contains a large library of step-by-step matching combinations. They are also conveniently listed for selection. For example, in a 2-section LC match, you can only use two topologies: lowpass type (series-IND+shunt-CAP) or highpass type (shunt-IND+series-CAP). As these are the only combinations, iMatch makes them both available in selection boxes while presenting schematic, frequency response, and Smith Chart impedance response. With a few mouse clicks you can see the difference between these circuits. The element values are optimally calculated and further changes are not necessary. For this reason, iMatch does not allow you to edit element values. There are enough matching types in the library to allow you to find a suitable solution. Fifty matching circuit types are currently available, so for any given design problem, you can always find a suitable matching type.

13.6.5.8. Smith Chart

The Smith Chart is a graphical representation of transmission line and impedance matching circuits. It is widely used in theoretical work, teaching, and understanding of how various electrical components change the effective input impedance and reflection of high-frequency networks. There are many textbooks and online material available that discuss how to use a Smith Chart.

In iMatch, the Smith Chart displays for completeness purposes. Its main use which exploits “how individual components move an input impedance around the chart at a single frequency” is replaced by the more useful “wideband frequency response”. The chart in iMatch shows input/output impedances across the selected frequency range. The following impedance traces always display:

  • Load impedance, set by clicking the Edit Terminations button

  • Complex conjugate of Load impedance

  • Source impedance, set by clicking the Edit Terminations button

  • Complex conjugate of Source impedance

  • Matching+Load impedance, the input impedance seen from the input of matching circuit towards the load

Additionally, you can add two optional traces representing the 2nd and 3rd harmonic response of the matching network, by clicking the Show/Hide Harmonics on Smith Chart ("H") button.

Each trace displays in a different color. A circle is drawn on one end of the traces to mark the minimum frequency of analysis.

Constant VSWR Circles

Constant VSWR circles are centered on the Smith Chart. As the name implies, at any point along its circumference, VSWR is constant. VSWR and return loss are related by the following equations:

VSWR = (1 + |S11|) / (1 - |S11|)

Return Loss = - 10 * log10 |S11|^2

The relationship between VSWR and RL is unique (single-valued). Both terms are used interchangeably in high-frequency circuit design.

In iMatch, constant VSWR circles that correspond to four major return loss values display. If the impedance stays within the circles, they have better return loss than the circle itself. The aim, therefore, is to contain the impedance trace within the desired constant VSWR circle.

You can toggle constant VSWR circles on a Smith Chart by clicking the Show/Hide Constant VSWR Circles button (the first) in the following group of buttons.

Constant Resistance Circles

Constant resistance circles are centered along the horizontal axis. As the name implies, at any point along its circumference, the resistive part of impedance is constant. The points where the circles cross the horizontal line are “purely” resistive. The circle that passes through the center of a Smith Chart is unity resistance (R=1).

You can toggle constant resistance circles on a Smith Chart by clicking the Show/Hide Constant Resistance Circles button (the second) in the following group of buttons.

Constant Reactance Circles

Constant reactance circles are centered along the vertical axis that intersects the right-most point of the horizontal axis on a Smith Chart. As the name implies, at any point along its circumference, the reactive part of the impedance is constant. These circles do not cross the horizontal line which is purely resistive. In the Impedance Chart, the top semicircle is inductive, so the circles represent constant inductance circles. Likewise, the circles in the bottom semicircle are constant capacitance circles.

You can toggle constant reactance circles on a Smith Chart by clicking the Show/Hide Constant Reactance Circles button (the third) in the following group of buttons.

Constant Q Circles

Constant Q circles are centered along the vertical axis that intersects the center of a Smith Chart. Q is inversely related to the frequency bandwidth of the network. For wideband circuits, it is desirable to stay within the specified constant Q circle. The relationship between Q and bandwidth is not simply interpreted. It is better to use rectangular Insertion Loss/Return Loss charts to understand bandwidth.

Constant Q circles are displayed for completeness. You can toggle constant Q circles on a Smith Chart by clicking the Show/Hide Constant Q Circles button (the fourth) in the following group of buttons.

13.6.6. Impedance Matching Types

This section lists impedance matching types currently available in iMatch. To explain matching types, a simple matching example with R1=50, R2=25 is presented. Matching is performed at 500 MHz. For reactive terminations, a reactance cancellation element is included in the matching circuit. Some of the matching types use transmission lines to perform the reactance cancellation, so no extra element is produced.

13.6.6.1. Manual

Manual matching is provided for complementary purposes for those who prefer performing impedance matching at single spot frequencies. In this mode, a Manual Matching dialog box displays to specify matching elements.

At the top of the dialog box, matching elements display in order from source to the load side. This dialog box copies the last matching network when it displays the first time.

You can use the Add, Insert, Replace, and Del buttons to modify the matching elements. When an element type is selected in the list box at the bottom of the dialog box, the relevant parameters L, C, Zo, and EL of the matching element are editable. The Up and Down buttons are used to move the position of the selected matching element in the list.

After any changes to the matching network, the main Matching dialog box updates the schematic drawing and the corresponding responses.

13.6.6.2. Lumped Element: L/Pi/Tee Type

These matching types are the simplest 2-element or 3-element sections. Although simple, they provide enough matching for many HF and VHF applications.

L-section LP (Lowpass)

This 2-section lumped element type provides an infinite return loss at the desired matching frequency, and maintains a lowpass frequency response. Due to the Shunt-Series element layout, this circuit is also called "L-section". The position of the series inductor depends on the R1/R2 ratio. If R1 is smaller than R2, then the series inductor is positioned to the left of the shunt capacitor.

This design is a unique solution of impedance values; you can only edit the center frequency. The circuit is DC shorted between the terminations and DC isolated from ground.

L-section HP (Highpass)

The highpass version of the LP type uses a series capacitor and shunt inductor. The circuit is DC isolated between terminations and DC shorted to ground.

Pi-section CLC (Capacitor–Inductor–Capacitor)

This circuit with two shunt arms and a series element resembles the math symbol π, hence the name. CLC refers to "Capacitor-Inductor-Capacitor". This type of topology is similar to a lowpass filter. The frequency response is lowpass or quasi-lowpass with wideband analysis. The circuit is a DC short between terminations and DC isolated from ground.

Pi-section LCC (Inductor–Capacitor–Capacitor)

This is another Pi-circuit with a highpass/quasi-highpass/bandpass response. LCC refers to "Inductor-Capacitor-Capacitor". The circuit is DC isolated between terminations and DC shorted to ground.

Pi-section CLL (Capacitor–Inductor–Inductor)

This is a Pi-circuit with a moderate bandpass response. CLL refers to "Capacitor-Inductor-Inductor". The circuit is DC shorted between terminations and DC shorted to ground.

Tee-section CCL (Capacitor–Capacitor–Inductor)

This circuit with two series arms and a shunt element looks like a Tee (letter "T"), hence the name. CCL refers to "Capacitor-Capacitor-Inductor". This type of topology produces a moderate bandpass response, similar to the response of the Pi-section CLL. The circuit is DC isolated between terminations and DC isolated from ground.

Tee-section LCL (Inductor–Capacitor–Inductor)

This Tee-circuit with a lowpass/quasi-lowpass response is similar to the Pi-section CLC. LCL refers to "Inductor-Capacitor-Inductor". The circuit is DC shorted between terminations and DC isolated from ground.

Tee-section LLC (Inductor–Inductor–Capacitor)

This is a Tee-circuit with a bandpass/quasi-highpass response similar to the Pi-section LCC. LLC refers to "Inductor-Inductor-Capacitor". The circuit is DC isolated between terminations and DC shorted to ground.

13.6.6.3. Lumped Element: N-section

Customized solutions up to 4th order are already provided via dedicated buttons. iMatch also provides generic lowpass type solutions for higher orders. When you select N-section, the parameter # sections under Specifications is also editable.

Max.Flat

A Maximally-flat filter provides the flattest passband response at a given frequency. In his September, 1965 MTT article, Cristal provided lowpass prototype tables up to 10th order. iMatch uses those table values and interpolates them for the required impedances.

To calculate the element values, the terminations are first converted to their real-form by performing the selected reactance cancellation method. After obtaining the two real source and load impedances, Z1/Z2 ratio is then looked up in the tables and interpolated for the nearest impedance ratio, and g-values and element values are calculated.

13.6.6.4. Lumped Element: 3-section

3-section lumped element matching circuits are obtained by cascading three lowpass or highpass matching sections. At the frequency of matching, the return loss is very large, so in the vicinity of Fo, a bandpass response is obtained. In a wider spectrum, depending on the number of contributing sections, 3-section matching circuits can have either of lowpass, highpass or bandpass responses. The following figure shows a typical matching circuit.

The matching circuit contains HP-LP-HP sections. As the figure suggests, each section is designed to match an impedance level to another one. The first CAP-IND section matches R1 to Rm1, the middle IND-CAP section matches Rm1 to Rm2, and the third IND-CAP section matches Rm2 to R2. Only R1 and R2 are specified by design; you can freely select Rm1 and Rm2. The optimum solution is found when R1/Rm1 = Rm1/Rm2 = Rm2/R2.

You may want to choose different impedance levels to trim the circuit response and adjust element values, however, so at least one of these intermediate values should be left to choice.

iMatch allows implicit specification of Ra by specifying the Q for the last section. Conventionally, Q gives a better indication of matching bandwidth. Q and Ra are related by the equation Rm2 = R2 * (Q*Q + 1).

After Rm2 is found, Rm1 is calculated from Rm1 = (R1 * Rm2)^0.5 and all three sections are designed using these impedances.

These matching types usually result in six matching elements. In some cases, Q specification yields inner sections that need mirroring. As a result, two parallel or series elements may occur which are combined in the end, and five or less elements may exist in the final design.

LP-LP-LP (Lowpass–Lowpass–Lowpass)

Due to all three sections having lowpass characteristics, this matching circuit has more lowpass response than bandpass. The circuit is DC shorted between terminations and DC isolated from ground.

LP-LP-HP (Lowpass–Lowpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations and from ground.

LP-HP-LP (Lowpass-Highpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

LP-HP-HP (Lowpass–Highpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-LP-LP (Highpass–Lowpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-LP-HP (Highpass–Lowpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-HP-LP (Highpass–Highpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-HP-HP (Highpass-Highpass-Highpass)

Comprised of three highpass sections, this matching circuit has more highpass response than bandpass. The circuit is DC isolated between terminations but DC shorted to ground.

13.6.6.5. Lumped Element: 4-section

4-section lumped element matching circuits are similar to 3-section circuits, except that they have one more section, and therefore, potentially wider bandwidth. Much of the explanation for 3-section circuits is valid for 4-section circuits.

As in 3-section circuits, Q is specified for the last section which matches Rm3 and R2. This Q specification offers flexibility for impedance levels. Once Rm3 is determined from Q and R2, the other intermediate levels are found with R1/Rm1 = Rm1/Rm2 = Rm2/Rm3.

LP-LP-LP-LP (Lowpass–Lowpass–Lowpass–Lowpass)

Comprised of all lowpass sections, this matching circuit has more lowpass response than bandpass. The circuit is DC shorted between terminations but DC isolated from ground.

LP-LP-LP-HP (Lowpass–Lowpass–Lowpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

LP-LP-HP-LP (Lowpass–Lowpass–Highpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

LP-LP-HP-HP (Lowpass–Lowpass–Highpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

LP-HP-LP-LP (Lowpass–Highpass–Lowpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

LP-HP-LP-HP (Lowpass–Highpass–Lowpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

LP-HP-HP-LP (Lowpass–Highpass–Highpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

LP-HP-HP-HP (Lowpass–Highpass–Highpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-LP-LP-LP (Highpass–Lowpass–Lowpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-LP-LP-HP (Highpass–Lowpass–Lowpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-LP-HP-LP (Highpass–Lowpass–Highpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-LP-HP-HP (Highpass–Lowpass–Highpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-HP-LP-LP (Highpass–Highpass–Lowpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-HP-LP-HP (Highpass–Highpass–Lowpass–Highpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-HP-HP-LP (Highpass–Highpass–Highpass–Lowpass)

Comprised of lowpass and highpass sections, this matching circuit has a bandpass response. The circuit is DC isolated between terminations but DC shorted to ground.

HP-HP-HP-HP (Highpass–Highpass–Highpass–Highpass)

Comprised of all highpass sections, this matching circuit has more highpass response than bandpass. The circuit is DC isolated between terminations but DC shorted to ground.

13.6.6.6. Distributed/Mixed Element: TL+Stub

TL+stub matching circuits use distributed or mixed elements to achieve impedance matching at UHF and microwave frequencies. Transmission lines and stubs are mostly printed circuits, requiring you to add only one or two shunt capacitors. Because of their simplicity to construct and tune (trimming lines and stubs), they are by far the most used matching circuits at high frequencies.

The transmission line element near the termination is also used to manipulate and/or cancel reactance, so Reactance Cancellation is not needed for these matching types. In iMatch, this option is disabled to avoid any confusion.

Shunt OST + TL (Shunt Open Stub + Transmission Line)

This distributed element matching network uses a transmission line and an open circuited stub. The same impedance is used for the line and stub, AS specified in Reactance Cancellation. The circuit is DC shorted between impedances. Because it is DC isolated from ground, it is suitable for amplifier input and output matching.

Shunt SST + TL (Shunt Shorted Stub + Transmission Line)

This distributed element matching network uses a transmission line and a short circuited stub. The same impedance is used for the line and stub, as specified in the Reactance Cancellation group. The circuit is DC shorted between terminations. Because it is DC shorted to ground, it is not suitable for amplifier input and output matching.

Shunt IND + TL (Shunt Inductor + Transmission Line)

This mixed element matching network uses a transmission line and a shunt inductor. The transmission line impedance is specified in Reactance Cancellation. The circuit is DC shorted between terminations. Because it is DC shorted to ground, it is not suitable for amplifier input and output matching.

Shunt CAP + TL (Shunt Capacitor + Transmission Line)

This mixed element matching network uses a transmission line and a shunt capacitor. The transmission line impedance is specified in Reactance Cancellation. The circuit is DC shorted between terminations. Because it is DC isolated from ground, it is suitable for amplifier input and output matching.

Series IND + TL (Series Inductor + Transmission Line)

This mixed element matching network uses a transmission line and a series inductor. The transmission line impedance is specified in Reactance Cancellation. The circuit is DC shorted between terminations. Because it is DC isolated from ground, it is suitable for amplifier input and output matching.

Series CAP + TL (Series Capacitor + Transmission Line)

This mixed element matching network uses a transmission line and a series capacitor. The transmission line impedance is specified in Reactance Cancellation. The circuit is DC isolated between impedances. Because it is DC isolated from ground, it is suitable for amplifier input and output matching. The high impedance DC bias line should be connected to the transmission line, however.

Double Shunt OST + TL (Shunt Open Stub + Transmission Line + Shunt Open Stub + Transmission Line)

This distributed element matching network is obtained by applying Shunt OST + TL twice. An intermediate impedance level Rm = (R1*R2)^0.5 is assumed and the two sections are designed to match R1 to Rm and Rm to R2. The transmission line and stub impedances are all the same and are specified in Reactance Cancellation. The circuit is DC shorted between terminations. Because it is DC isolated from ground, it is suitable for amplifier input and output matching.

Double Shunt CAP + TL (Shunt Capacitor + Transmission Line + Shunt Capacitor + Transmission Line)

This distributed element matching network is obtained by applying Shunt CAP + TL twice. An intermediate impedance level Rm = (R1*R2)^0.5 is assumed and the two sections are designed to match R1 to Rm and Rm to R2. The transmission line impedances are the same and the value is specified in Reactance Cancellation. The circuit is DC shorted between terminations. Because it is DC isolated from ground, it is suitable for amplifier input and output matching.

Double TL (Transmission Line + Transmission Line)

This distributed element matching network is obtained by cascading two transmission lines. You specify the first transmission line impedance near the termination in Reactance Cancellation. Its line length is calculated to convert a reactive termination to a real impedance (Rm). In the previous example, an inductor is added to the termination to make it reactive. If the termination is purely resistive, this transmission line is simply omitted. The next transmission line is a quarterwave length line and its impedance is calculated from Zo = (R1*Rm)^0.5.

The circuit is DC shorted between terminations. Because it is DC isolated from ground, it is suitable for amplifier input and output matching.

Single TL (short) (Single Transmission Line – Short Line)

Of all the matching networks available, the single transmission line is the only type that does not offer a perfect match at the specified frequency. Its inclusion is only due to its simplicity, which may be preferred for “good-enough” return loss. Given the characteristic impedance, the line length is calculated for the best return loss at the specified frequency. Because of periodicity in a distributed element circuit, line length can be increased in 180-degree increments with the same response. If the line length is too small, you may prefer the Single TL (long) solution which exploits this idea.

The circuit is DC shorted between terminations. Because it is DC isolated from ground, it is suitable for amplifier input and output matching.

Single TL (long) (Single Transmission Line - Long Line)

Of all the matching networks available, the single transmission line is the only type that does not offer a perfect match at the specified frequency. Its inclusion is only due to its simplicity, which may be preferred for “good-enough” return loss. Given the characteristic impedance, the line length is calculated for the best return loss at the specified frequency.

The circuit is DC shorted between terminations. Because it is DC isolated from ground, it is suitable for amplifier input and output matching.

13.6.6.7. Distributed Element: Multiple TL

Multiple transmission line matching circuits are used to obtain wideband matching for large impedance ratios. In addition to the application frequency, you also specify the number of sections. Higher sections result in wider bandwidth but larger circuits. Types in this category yield similar responses with subtle differences as explained for each type. All of the types are DC shorted between terminations and DC isolated from ground, so suitable for amplifier input and output matching.

Multi TL matching circuits do not inherently cancel the reactive parts of terminations, so Reactance Cancellation options are available and utilized if the terminations are reactive.

Middle Impedance

This matching network uses the middle impedance method, where intermediate impedance levels and line impedances are calculated from application of the same formula Rm = (Rj*Rk)^0.5, where Rj and Rk belong to impedances or impedance levels of the previous and next sections. Matching performance is similar to the Binomial type.

Binomial

This matching network uses the middle impedance method, where intermediate impedance levels and line impedances are calculated from a binomial formula, which gives maximally flat response for 90-degree line lengths. Matching performance is similar to the Middle Impedance type.

Klopfenstein Taper

Among multi TL types, the Klopfenstein taper provides the widest matching bandwidth for a given total line length. You specify the total line length (EL). Shorter EL causes wider bandwidth, however the lower cutoff frequency of matching increases by decreasing EL. The return loss is uniform across the bandwidth. Klopfenstein tapers can be designed for any return loss.

Hecken Taper

The Hecken taper is specified and designed similar to Klopfenstein tapers, but provides more return loss around the matching frequency and less return loss away from the matching frequency.

Exponential Taper

The exponential taper is included for completeness. The impedance values are calculated to fit an exponential increase and the line length is obtained by dividing the specified EL into the number of sections. The matching performance is not significantly better or worse than other multi TL types.

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