All posts by Martin Blustine

I studied physics and went on to work in infrared optics, millimeter wave and microwave engineering until retirement. My interests lie in teaching, music, radio astronomy, infrared systems and microwave and antenna engineering. I enjoy writing technical papers about ham radio topics. When I am not operating CW, I enjoy homebrewing ham gear and restoring vintage HP and Agilent test and measurement equipment.
Antennas, Featured, General

Matching to the Complex Load Impedance of a Shortened, Non-Resonant Antenna – Part I

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Matching to the Complex Load Impedance of a Shortened, Non-Resonant Antenna – Part I

Introduction

A common impedance matching problem is that of matching a 50 ohm transmitter to a shortened non-resonant antenna. Examples of non-resonant antennas are the 23-foot (7.01m), and the 43-foot (13.1m) backyard vertical antennas. These antennas have something in common. They exhibit high capacitive reactance.

It is hoped that this multi-part article will provide the reader with the tools necessary to contend with this common antenna matching problem.

Part II of this article will discuss impedance matching to a 43-foot backyard vertical antenna using a 1:1 UNUN and an autotransformer[1].

The high voltages developed in these matching networks will be the subject of Part III of this article[2].

Example 1: 23-Foot Backyard Non-Resonant Vertical Antenna

A 23-foot backyard vertical with numerous radials exhibits an impedance of 19.79 – j631.9 ohms at 3.6 MHz at its base.

For this exercise, we don’t care about the number of radials, conductor losses, ground losses, and reflected power that all figure into efficiency. All we care about is matching to this complex impedance.

Unmatched VSWR

Let’s calculate the unmatched VSWR at the base of our 23-foot backyard vertical before we apply matching techniques. The load impedance that must be matched is assumed to be

The source impedance of the transmitter is given by

To calculate VSWR, we need to relate these two complex quantities to the magnitude of the reflection coefficient,

Those of us who own nanoVNAs have become used to the term S11, which is the input voltage reflection coefficient. By definition

This is a complex number that has to be rationalized before its magnitude can be found.

We should begin by combining terms where possible.

VSWR: Method I – Rectangular Form

Rationalize the denominator.

Like terms are combined to find the reflection coefficient.

The magnitude of the reflection coefficient is obtained from

Finally, the VSWR is computed from

The VSWR is 406:1 due to the high value of capacitive reactance.

VSWR: Method II – Polar Form

As before, and after combining terms, we begin with

and let

By dividing Z1 by Z2, we obtain

Notice that when the angle is moved from the denominator to the numerator, the sign changes.

We may stop here since we already have what we need

or, for the exercise, we may convert back to rectangular form using the Euler identity and arrive back at the same place.

Rectangular and polar forms lead to the same result.

The high VSWR is due to the high value of capacitive reactance of the unmatched load impedance.

Matching Techniques

When faced with problems like these, it is often easier to break the problems down into more manageable steps.

How to match the real part of the load impedance was the subject of an earlier paper[3] but let’s review the procedure for this case.

We begin by inspecting the impedance to see what we can learn about it. The real part is 19.79 ohms. This resistance, RL, is smaller than the real 50 ohm transmitter impedance, RS. If we were to use a simple LC matching network, an L-network, we can see from Figure 1 that there are four possible topologies: two low-pass topologies and two high-pass topologies[4]. Notice that the low-pass topology is capable of conducting DC from input to output. This is not possible with the high-pass topology that blocks DC with a series capacitor. We begin by picking the low-pass topology in Figure 1(b) for which RS > RL.

Figure 1. L-Matching Network Topologies. Source and load impedances are real. Reproduced under CC BY-NC by permission from Michael Steer, North Carolina State University.

It is instructive to work through low-pass and high-pass topologies to illustrate how these problems are solved. It is important to note that all of these solutions result in an impedance match for a narrow band of frequencies. If multi-band operation is required, the use of multiple matching networks or the use of an antenna tuner (preferably a remote one) will be necessary.

Other matching techniques are possible, such as center loading and top loading but we will limit the discussions in Part I, Part II, and Part III to base loading.

Example 1: Low-Pass Topology

We begin by writing down what we know,

Step 1

We set the imaginary part of the load impedance, ZL, to zero for Step 1 of the solution. We will revisit the reactive part in Step 2 of the solution.

Thus,

 

We make use of Figure 1(b) to compute the unloaded Q for the L-matching network

and

where

Substituting, we have

Also,

At 3.6 MHz, the matching network inductance is

and the matching network capacitance is

Step 2

Our matching solution is incomplete until we cancel the remaining part of the load impedance that we ignored earlier, i.e., the imaginary part of the load impedance,
-j631.9 ohms, must be canceled to achieve a match. The secret to achieving a match is in finding a value of inductance that resonates with the capacitive reactance. Once completed, the series combination of load capacitance and added resonant inductance will result in zero reactance at the resonant frequency. We remember that for series resonance, ignoring any losses in the inductor and capacitor, the LC resonant pair looks like a short circuit at the design frequency. That’s exactly what we want – we want the load capacitance and the additional inductor to look like zero ohms at resonance. Of course, real inductors have series resistance due to the wire and capacitors have dielectric losses but for this exercise, we assume that they do not.

Thus, at resonance we have

where

C is the capacitance equivalent to the complex part of the load impedance, not the matching network, C‘, in units of Farads.

Thus,

The value, L”, is added to L‘. This will result in a new value for the L-matching network inductor, L”’

We don’t have to add the two together, and it may be easier to think about what each of the inductances does if we leave them as separate components.

This matching circuit may be simulated using RFSim99[5]. The circuit model is shown in Figure 2. The inductors L‘ and L” are drawn separately for emphasis. (Two inductors in series may be added.)

Figure 2. Low-Pass L-Matching Circuit. The inductor, L‘=1.08 μH, and added resonating inductor, L”=27.94 μH, are shown separately for clarity.

Return Loss and VSWR

In the VSWR section, above, we calculated the VSWR from

We may also calculate VSWR from the return loss, RL, directly from

where we have divided the return loss by 20 because the return loss is the voltage return loss.

Let’s calculate the VSWR for our simulation, where the return loss is 50 dB.

The resulting return loss for the low-pass matching circuit is shown in Figure 3. The 2:1 bandwidth of the matching network is ~78 kHz. The return loss is better than 50 dB at 3.601 MHz, or better than 1.01:1.

Figure 3. Return Loss for Low-Pass Matching Circuit. The 2:1 bandwidth of the matching network is ~78 kHz. The return loss is better than 50 dB at 3.6 MHz, or better than 1.01:1.

It may be concluded that this two-step matching technique for a low-pass matching network works quite well for our shortened antenna on the 80m band.

Example 2: High-Pass Topology with Series to Parallel Load Conversion

For the high-pass L-matching network Figure 1 shows that two topologies are possible. The one chosen would depend on how the capacitive reactance of the load is to be canceled.

There are two ways to accomplish this depending on where the inductance is in the matching network. The inductance in the high-pass configuration is always parallel at the input or parallel at the output. The position of the inductor depends on which is larger, RS or RL. The matching L-network inductor is always closest to the larger of the two as is seen in Figure 1.

The capacitance in the load is normally thought to be in series with the load resistance. This capacitive reactance could be canceled with a series inductor added to the L-matching network but there is a more interesting way to do it.

If the series RC load combination was converted to parallel form, as is often done for us on our VNAs, it would be observed that the new parallel resistance has a value that is much higher than the source impedance. By necessity, that would place the inductor in the high-pass L-matching network in parallel with the parallel capacitance of the load.

If we were to think about parallel resonance, and neglecting any losses in the load capacitor and resonating inductor, at resonance the pair looks like an open circuit. Then, the L-matching network just sees the real part of the load impedance.

The solution begins by converting the load from series form to parallel form.

Step 1

As it turns out, there is a transformation between series and parallel circuits that works at a single frequency. As was the case for the low-pass L-matching network, we ignore the reactive part of the load, initially. and incorporate it into the solution later. The series to parallel transformation works when

and

and

Then,

and

where

The Q-value is higher than we would like, but let’s proceed to see what happens.

There is enough information to derive the values

At 3.6 MHz the parallel load capacitance becomes

We observe that while the load resistance changes a great deal, the capacitance value hardly changes at all.

Step 2

Next, the real source impedance of the transmitter, 50 ohms, must be matched to the real part of the parallel load impedance. For this case we have determined by series to parallel transformation that

To keep our notation understandable, please note that for this section, RP is substituted for RL.

Since RP is greater than RS, we must use the correct high-pass equations for unloaded Q given in Figure 1(c).

Substituting, we find that

We have the values of capacitance and inductance that will match the pure 50 ohm source impedance to a 20158 ohm load resistance.

Step 3

Now it is time to resonate the parallel load capacitance that we calculated with a parallel inductor that will be added to our matching circuit. The value of this inductor will have a value that is similar to the one that we computed for the low-pass topology. We use the same equation for resonance as before

Figure 4 shows the model for the high-pass topology. A parallel inductor is introduced at the output of the L-matching network to resonate out the parallel capacitor in the load.

We don’t have to do it, but for practice, let’s go through the steps to combine the matching network inductor in parallel with the resonating inductor

Figure 4. High-Pass L-Matching Network Topology. (Top) L-matching network with a separate resonating inductor as marked. (Bottom) L-matching network, where the L-matching network and resonating inductor have been combined in parallel to produce a single 17.16 μH inductance.

Once the simulation is run, Figure 5 shows that the high circuit Q results in a narrow 2:1 bandwidth, ~ 48 kHz. The 20158 ohm resistor is responsible for this.

Figure 5. High-Pass L-Matching Network Topology Return Loss. The return loss at 3.6 MHz is better than 50 dB demonstrating a VSWR of better than 1.01:1 over a narrow 48 kHz 2:1 VSWR bandwidth.

We conclude that the conversion to the parallel load configuration has resulted in an unloaded circuit Q that is high. This results in a narrower 2:1 bandwidth. The calculation is now repeated for the original series load to which will be added a series resonating inductor. Let’s see if the bandwidth can be improved.

Example 3: High-Pass Topology with Series RC Load

We return to the original series RC load impedance and choose the high-pass topology for the L-network.

Step 1

The high-pass solution for the series RC load begins with the following assumptions

The solution will ignore the imaginary reactance of the load impedance, initially. It will be used later.

The defining equations from Figure 1(d) for a high-pass L-matching network where the load resistance, RL, is smaller than the source resistance, RS, and where Q is the unloaded Q are given by

and

where

Substituting, we have

Also,

At 3.6 MHz, the matching network inductance is

and the matching network capacitance is

The value of unloaded Q is low, and the matching capacitance is high.

Step 2

The capacitive reactance of the load impedance has not yet been canceled as it was ignored in Step 1. A way must be found to cancel this reactance, but we observe in Figure 6 that the high-pass topology separates the load capacitance from the L-matching network shunt inductance, which is at the input.

Let’s try adding a series resonating inductance at the output of the L-matching network. That should work even though this inductance may not be combined with the L-matching network inductor.

The series load capacitance is resonated with a series inductor that will be added to our matching circuit. The value of this inductor is given by

The check for this topology is provided by the circuit model of Figure 6. A resonating inductance has been added in series with the L-matching network. It is not convenient to combine this series inductance with the parallel inductance at the input.

Figure 6. High-Pass L-Matching Network with Series Resonating Inductance Circuit Model. A resonating inductance is added in series with the L-matching network. It may not be combined with the parallel inductor at the input.

The results of this topology are shown in Figure 7. The return loss for this circuit model at 3.6 MHz is better than 49 dB for a VSWR or 1.01:1. The 2:1 VSWR is 78 kHz just as it was for the low-pass solution.

Figure 7. High-Pass L-Matching Network with Series Resonating Inductance Return Loss. The proof of this topology is evident from the plot. The return loss is better than 49 dB for a VSWR of better than 1.01:1 at 3.6 MHz. The 2:1 bandwidth is ~ 78 kHz which is the same as it was for the low-pass configuration.

The series RC load configuration is preferable over the parallel RC load configuration.

It may be concluded that this two-step matching technique for a high-pass matching network works quite well for the 80m band.

Conclusions

In Part I of this article we have used simple L-matching networks with additional resonating elements to match complex loads that possess capacitive reactance. This technique works for antennas that are too short. For antennas that are too long, the antenna load will also be complex but the resonating element required is a capacitor that cancels the inductive reactance of the complex load.

In Part II we will explore a different technique for matching to the complex load presented by a 43-foot backyard vertical antenna. The matching network will consist of a 1:1 UNUN followed by an autotransformer.

In Part III we will discuss the high voltages encountered in highly reactive loads. This occurs when antennas are far too long, or far too short.

References

[1] Salas, Phil, 160 and 80 Meter Matching Network for Your 43 foot Vertical — Part 2, QST, January 2010, pp. 34-37. http://www.arrl.org/files/file/QST%2520Binaries/QS0110Salas.pdf

[2] Ibid.

[3] Blustine, Martin, Highly Efficient L-Matching Networks for End-Fed Half-Wave Antennas, June 11, 2022. https://www.n1fd.org Add Contact Form /2022/06/11/l-matching-networks/

[4] Reproduced under CC BY-NC by permission from Michael Steer, North Carolina State University, LibreTexts™, 6.4: The L-Matching Network, https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Electronics/Microwave_and_RF_Design_III_-_Networks_(Steer)/06%3A_Chapter_6/6.4%3A_The_L_Matching_Network

[5] RFSim99, Stewart Hyde, author, 1999. https://www.ad5gg.com/2017/04/06/free-rf-simulation-software/

 

Antennas, Featured, General

Temporary 20m EFHW Vertical Installation

I’ve been off the air since moving back to NH in 2020. Since the landscaping has not been completed on the property, it has been impossible to install the radials for a  6-BTV vertical. Radials don’t fare well under the treads of a Bobcat.

A collection of single-band, matched, end-fed half-wave (EFHW) antennas was constructed while I was living in FL. All of these antennas underwent testing on an antenna range consisting of three 10m tall masts spaced 70 ft apart.  These antennas were matched with L-networks. The test results were reported in a separate article[1].

Seeing that July 4th weekend was approaching, I was eager to get on the air for a few days before the landscaper arrived. I decided on a 20m EFHW vertical that makes use of some of the guy ropes that were prepared for FL antenna testing. Figure 1 shows the installation of the 12.5m high telescoping fiberglass mast.  The mast is anchored with a tilt-over base mounting plate described in a separate article[2]. Guying is provided at two levels. The guying radius is 25 ft. Guy anchoring is accomplished with polycarbonate Orange Screws[3]. While these anchors work well in FL sand, they do not work quite as well in rocky New England soil. I managed to snap one of them off in the process of screwing it into the ground.

My favorite knot for adjusting the guy rope tension is the taut-line hitch. I used the taut-line hitch on the FL antenna range for three weeks, and the anchor screws came loose before any of the taut-line hitches did.

20m end-fed half-wave (EFHW) vertical

Figure 1. 20m L-Network Matched EFHW Vertical. The wire antenna and matching network is fastened to the fiberglass mast with rubber bongo ties. The mast height is 12.5m (41 ft). Base anchoring is accomplished with a hinged, tilt-over base mounting plate that was described in another article. Please click on the photo to enlarge it.

The antenna counterpoise consists of a 3 ft (~ 1m) section of outer coax shield, Figure 2. A line choke is inserted after this 3 ft section of coax to terminate the counterpoise. The remainder of coax to the shack is made up of a 40 ft long section of RG-8X.

Figure 2. Matching Network, Coaxial Shield Counterpoise and Line Choke. The matching network was designed for 14.1 MHz. Since the matching network has a wide bandwidth, the antenna wire was cut slightly longer to resonate at the very bottom of the CW band. Please click on the photo to enlarge it.

A Smith Chart is plotted in Figure 3. It shows that the antenna match over the entire band is well within the 2:1 VSWR circle.

Figure 3. Smith Chart for 20m L-Matched EFHW Antenna. A match better than 2:1 match is achieved over the entire 20m band. The antenna wire was cut longer to provide the best match at 14.025 MHz. Please click on the photo to enlarge it.

The VSWR performance is plotted in Figure 4. The matching network consists of a lowpass L-network consisting of a series inductor followed by a shunt coaxial capacitor. The antenna wire has been cut to resonate at 14.025 MHz since I enjoy operating in the bottom 50 kHz of the 20m CW band. It’s not that the VSWR performance was that bad but I just could not understand why the antenna wasn’t achieving a near-perfect 1:1 match. I turns out that the residual mismatch is in the Polyphaser lightning arrestor located in the service entrance panel.

Figure 4. 20m VSWR Plot. The L-matching network exhibits wide bandwidth and good efficiency. The antenna wire is cut to resonate at the very bottom of the CW band where I like to operate. The match is very good but not perfect. This was due to the residual VSWR in the lightning arrestor located in the service entrance panel. Please click on the photo to enlarge it.

I operated a simple station consisting of an ICOM 718 at 100W to make three consecutive CW contacts with French stations. The next three days should produce some interesting DX.

References

[1] Blustine, Martin, Highly Efficient L-Matching Networks for End-Fed Half-Wave Antennas, June 11, 2022. https://www.n1fd.org/2022/06/11/l-matching-networks/

[2] Blustine, Martin, Tilt-Over Bases for Antenna Masts That You Can Build, June 30, 2022. https://www.n1fd.org/2022/06/30/tilt-over-bases/

[3] https://www.orangescrew.com/

Featured, General

RFSim99 for Circuit Simulations

Introduction

Out of curiosity I recently downloaded a copy of RFSim99[1], authored by Stewart Hyde, to see what it could do and how easy it was to use. It runs as a standalone app. This is a very old program and much to the credit of the Gordon Hudson, AD5GG[2], an extracted version seems to run on Windows 11 in compatibility mode for Windows XP.

There were some posts online about how some of the user interface buttons would not appear until hovering the mouse over where the buttons should appear[3]. Another quirk had to do with plots not appearing after the simulation button was pressed. I encountered both of these quirks when I first installed the application, particularly after I had run my first simulation. After unzipping the program for a second or third time, I ran a Sample File from the Open file menu. It ran with no problem whatsoever. Next, I created a circuit model of my own, saved it and ran a simulation. This time everything worked and continues to work, as it should. If all else fails, you could try to alter the compatibility settings that may be found under Properties by right clicking the RFSim99 icon. I changed the settings to a later version of Windows XP. It is a good idea to save all circuit model files in a folder apart from the app in the event the program file folder has to be overwritten.

This application is highly intuitive and can be up and running in minutes. If you wish to rotate or flip a component, all you do is selected it and hit the space bar. The easiest way to correct an error is to select the mistake and hit delete on the keyboard.

Three simulations are the subject of this article; a 40m L-matching network for an EFHW antenna, a 2nd harmonic optimized lowpass filter and a Butterworth bandpass filter. These demonstrate different plotting features that are available in RFSim99; Smith Chart plots and rectangular plots, respectively.

This simulation app is very useful because it can return a full set of S-parameter results. We can derive anything and plot everything from the data set.

Simulation of a 40m L-Matching Network for EFHW Antennas

I decided to begin by running a simulation on a 40m L-matching network. These networks were the subject of an earlier article[4]. The matching network to be simulated is shown in Figure 1. A 50-ohm source drives an L-matching network that employs a lowpass topology. It is lowpass because the inductor is in series, and it will pass DC from input to output. A match from 50-ohms to 2450-ohms is required to match the high end impedance of an End-Fed Half-Wave (EFHW) antenna. Many of you will recognize this impedance transformation as being equivalent to the transformation performed by a 1:49 transformer. The design frequency used for the L-matching network was 7.15 MHz.

Figure 1. A 40m L-Matching Network. The lowpass topology is designed to match a 50-ohm transceiver to the 2450-ohm end impedance of an EFHW antenna at 7.15 MHz. The lowpass topology can be identified by the series inductor that can pass DC from input to output. Please note that there is a shunt capacitive element closest to the load. That means that this network is capable of transforming a higher load impedance down to a lower source impedance.

The results of the simulation are plotted using the Smith Chart option shown in Figure 2 that is available from a pull-down menu after running the simulation. The Smith Chart is simply a rectangular plot of real (resistance) and imaginary (reactance) values that has been cleverly constructed so that the reactance axes at infinity in the complex plane touch at the right hand side of the chart. It is an ingenious way of plotting axes that are infinite on a single sheet of paper. In order to do this the real resistance axis becomes more compressed to the right hand side of the chart, too.

If you are not familiar with Smith Charts, all of the values on the chart have been normalized to unity at the center of the chart. That makes it possible to use the chart to represent different characteristic impedances including 50-ohms. To get the final answer, we just multiply the number or numbers on the chart by the characteristic impedance. There is a cursor-slider on the bottom of each plot in RFSim99 that reads out the cursored values to the left and right sides of the chart. That is why there are no numbers displayed on the Smith Chart, itself.

Figure 2 consists of three plots at three different frequencies, 7.0 MHz, 7.15 MHz and 7.3 MHz, respectively. Since our antenna is too short at 7.0 MHz, the plot at a) exhibits capacitive reactance of ~14-ohms. At b) for the design frequency of 7.15 MHZ the antenna length is resonant and nearly zero reactance is exhibited. At c) for 7.3 MHz the plot exhibits inductive reactance of ~14-ohms because the antenna is too long. Please note that the impedances and admittances displayed to the left of each plot correspond to the position of the cursor. The series and parallel equivalent circuit values are displayed to the right of each plot.

Figure 2.  Smith Chart Plots of L-Network Impedance. The upper half of the Smith Chart plots inductive reactance while the lower half of the chart is capacitive reactance. The horizontal axis plots resistance with 50-ohms at the center of the chart. Please note where the cursor is and where the impedances are displayed  to the left of each plot. At a) for frequencies below the design frequency the antenna is too short, and the trace exhibits capacitive reactance. At b) the design frequency the reactance is nearly zero. At c) for frequencies above the design frequency of 7.15 MHz the antenna is too long, and the trace exhibits inductive reactance.

Simulation of a 2nd Harmonic Optimized Lowpass Filter

Ed Wetherhold, W3NQN, provided the filter prototype values for 2nd Harmonic Optimized Lowpass filters in his paper published in QST[5]. These designs with the addition of a filter for the newer 60m band were used to construct the 10-band lowpass filter bank shown in Figure 3 for use in a homebrew QRP transceiver under construction. Hans Summers at QRP Labs[6] was kind enough to provide bare filter printed circuit boards for the project. The motherboard consists of printed circuit coplanar waveguide designed on EasyEDA[7]. Relay switching provides high isolation and a primitive relay clacking sound.

Figure 3. A 10-Band 2nd Harmonic Optimized Lowpass Filter Bank for QRP Use. A 10-band filter bank was constructed on a coplanar waveguide motherboard. Switching is accomplished with inexpensive Arduino relay boards. A complementing 10-band bandpass filter bank completes the set.

The circuit model for the 2nd harmonic optimized 40m lowpass filter is shown in Figure 4. No changes were made to the component values appearing in the original article. A parallel resonant LC in the center of the schematic resonates at the 2nd harmonic, 14.4 MHz. This serves as a high impedance at the 2nd harmonic.

Figure 4. Circuit Model for 40m Lowpass Filter Simulation. No changes were made to the original component values in this simulation. Please note the LC circuit at the center of the schematic. It is designed to resonate at the second harmonic, 14.4 MHz. This serves as a high impedance at the 2nd harmonic.

The results of the simulation are provided in Figure 5 for filter attenuation and return loss in the passband and 2nd harmonic stopband. A return loss of 29 dB corresponds to a VSWR better than 1.1:1. The attenuation at the 2nd harmonic of the 40m band will far exceed the FCC requirement of 43 dB below the mean power of carrier emission.

Figure 5. Simulation for the 2nd Harmonic Optimized 40m Lowpass Filter. The cursor shows where the measurement values to the left and right hand side of the plots originate; at a) the values at 7.0 MHz, at b) the values at 7.3 MHz, at c) the values at the 2nd harmonic of 7.0 MHz, at d) the values at the 2nd harmonic of 7.3 MHz. S11 is the return loss trace while S21 is the transmission trace. A return loss of 29 dB corresponds to a VSWR better than 1.1:1. The attenuation at the 2nd harmonic of the 40m band will far exceed the FCC requirement of 43 dB below the mean power of carrier emission.

Simulation of a Butterworth Bandpass Filter

A simulation was run on a design provided by Lew Gordon, K4VX (SK), in his QST article[8]. A Butterworth bandpass filter, a.k.a. maximally flat filter, exhibits no ripples in its passband. Consequently, the stopband attenuation is more gradual than it is for other filter prototypes. (The Bessel filter also exhibits no passband ripple.) Figure 6 shows model employed for the 5-pole Butterworth bandpass filter simulation for the 40m band.

Figure 6. Simulation Model for a 40m 5-Pole Butterworth Bandpass Filter. A  5-pole filter is, essentially, two 3-pole filters back-to-back. The 2nf capacitor at the center of the filter is equivalent to 2 x 1nf capacitors in parallel. The 275nH inductor at the center of the filter is equivalent to 2 x 550nH inductors in parallel.

The 5-pole Butterworth bandpass filter was modeled in RFSim99, which resulted in the plots shown in Figure 7. Problems associated with the linear phase response of this filter are often avoided by deliberately making this filter very wide in which case only the center of the filter is used.

Figure 7. A 40m 5-pole Butterworth bandpass filter. At a) the filter return loss and transmission characteristics at 7.0 MHZ, at b) the filter return loss and transmission characteristics at 7.3 MHz, at c) the transmission characteristics and phase response of the filter. The filter is usually used at band center and within the linear phase region of its response. S11 is the return loss trace while S21 is the transmission trace. A return loss of 20 dB is 1.22:1.

Conclusions

The RFSim99 app is easy to use and configure. It runs reasonably well in Windows 11 when the compatibility mode for Windows XP is employed. It should run in earlier operating systems, too. There is no installer package for RFSim99 other than the one for Windows XP but AD5GG has extracted all of the files required to permit this program to run as a standalone app. Some common passive networks were analyzed that explore the capabilities of this software. Although the optimization utilities were not used for these analyses, they should be useful.

References

[1] Stewart Hyde, author, 1999.

[2] AD5GG, https://www.ad5gg.com/2017/04/06/free-rf-simulation-software/

[3] Ibid.

[4] M. Blustine, Highly Efficient L-Matching Networks for End-Fed Half-Wave Antennas, N1FD, June 11, 2022. https://www.n1fd.org/author/k1fql/page/5/

[5] Ed Wetherhold, Second-Harmonic-Optimized Low-Pass Filters, QST, February 1999, pp. 44-46. https://www.arrl.org/files/file/Technology/tis/info/pdf/9902044.pdf

[6] https://qrp-labs.com/

[7] https://easyeda.com/

[8] Lew Gordon, Band-Pass Filters for HF Transceivers, QST, September 1988, pp. 17-19, 23. https://www.arrl.org/files/file/Technology/tis/info/pdf/8809017.pdf

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