Education and Training

Some Fun with Boolean Algebra

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Introduction

This article will demonstrate how a simple logic problem may be solved using Boolean algebra.

Background

In the late 1950’s through the early 1970’s something called “New Math” [1] was introduced into grade school curricula under an initiative from the National Science Foundation (NSF). However, New Math was a misnomer, and nothing could be further from the truth. The math wasn’t new at all. It was just that an NSF committee had decided to introduce the elements of something called symbolic logic to school children. The elements of symbolic logic had been taught in college-level mathematics and philosophy courses for at least 175 years! Some of us even used a text, Symbolic Logic [2], written by the student of Bertrand Russell [3], Irving Copi [4].

During the cold war, it was thought that an introduction to the idea of logical reasoning would be more beneficial to young students than rote learning [5].  It was perceived that the United States had fallen horribly behind the Soviets in the areas of science and mathematics [6]. While that may have been the case, it turned out that in attempting to teach these more advanced concepts to the young, it may have set a backward trajectory for math and science education for many years to come.

Sensing that something was missing from my school curricula in 1963; I audited a summer school algebra course being taught in the neighboring town. It featured New Math. Having been schooled in Old Math; I soon understood of how little use New Math would be, i.e., until I began to play with logic circuits. The next time I saw the material was when I took a course in digital logic about 12 years later.

As I think back, maybe the time spent teaching New Math would have been better spent teaching a few skills in critical thinking?  By the 1970’s New Math had been, ironically, supplanted by Old Math, and textbooks that illustrated Venn diagrams on the covers had largely vanished.

As the late Tom Lehrer [7] of MIT (and later of UC Santa Cruz) sardonically reflected in his song lyrics:

New math, new-hoo-hoo math,
It won’t do you a bit of good to review math!
It’s so simple, so very simple,
That only a child can do it!

Enter George Boole

George Boole was a self-taught philosopher, mathematician and logician who served as the first professor of mathematics at Queens College, Cork, Ireland, in 1849 [8].

If you suffered through a course in symbolic logic, Boolean Algebra would have been one of the topics along the way.

Boolean logic symbols, and logic symbols in general, differ somewhat from those of grade school mathematics. For example, the plus symbol (+) stands for the logical symbol “OR”. We won’t have to introduce the added complexity of the OR symbol in this paper but it is really not hard to use. The dot symbol ( · ) that normally stands for multiplication stands for “AND”. This symbol along with something called an inverter will be used to solve the logic problem described in this paper. An inverter has the property that whatever is present at the input appears inverted at the output.

The Logic AND Gate

The logic AND gate is represented by the symbol shown in Figure 1. An accompanying  truth table for the AND gate is also shown. What is important to remember about AND gates is that if any statement is false, the whole statement is false. This may be inferred from the truth table. The cases shown are,

1.      A is true and B is false; the ANDing of the two, X, is false,

2.      A is false and B is true; the ANDing of the two, X, is false,

3.      A is false and B is false; the ANDing of the two, X, is false, and

4.      A is true and B is true; the ANDing of the two, X, is true.

Figure 1. The Logical AND Gate. If either of the inputs, A or B, is false, the output, X, is false. Please click on the figure to open it in a new window.

The Logic Problem to Be Solved

A QRP radio is under construction and Rick, N3FJZ, is the author of the software that operates many features of the radio and the display.  Rick maintains a website [9] as well as a YouTube channel [10]. Both sites are dedicated to homebrewing.

Since the software was intended for SSB operation, not CW, there is a logic state that is disallowed whenever band privilege restrictions are not entered as part of initial software setup. CW operation was never intended to be part of software setup [11].

There are two distinct modes of operation: general coverage receive and ham band transceive. If the receive frequency is set to anything other than a ham band, a general coverage command is asserted by the software. This command will switch out the low-pass filters, the power amplifier, and the band-pass filters. In their place, the command injects a bypass path around them. It is when the radio is in this state that Push-to-Talk (PTT) may be asserted, and the power amplifier will be biased. This should be disallowed.

A Possible Hardware Solution

Instead of modifying the code, a simple hardware modification is possible that will lock out the disallowed transmit state for the radio in general coverage mode.

It is known that a filter bypass flag appears on one of the Arduino microcontroller pins when the radio is tuned to anything other than one of the ham bands.

It is also known that a PTT flag appears on one of the Arduino microcontroller pins when the microphone PTT button is pressed or the PTT button on the control panel is pressed.

If we could use the filter bypass flag to inhibit transmit PTT whenever the radio is tuned to general coverage, the problem would be solved.

Figure 2 shows a truth table for the hardware solution for the problem as it is understood.

Figure 2. A Truth Table That Shows the Hardware Solution for the Problem as It Is Understood. All possible states of the PTT switch are shown in column A. All possible states of the Filter Bypass General Coverage command are shown in column B. Only one output state of X should be permitted. That is the one for which PTT is asserted and the radio is tuned within a ham band, either a SSB segment or a CW segment. All other cases shown in the truth table should be inhibited. Please click on the figure to open it in a new window.

The truth table in Figure 2 may be reduced to a single logical equation since we are only interested in the case for which X = 1. (any letter with a bar above it is the inverse of logical one, or zero). Thus,

This is read as A and B-bar equals X. The logic symbol that represents this is shown in Figure 3. Here we have drawn the symbol of a logical inverter to invert the symbol, B, to make it B-bar.

Figure 3. Simple Logic Circuit That Will Solve the Problem. For the single case of interest, A enters one of the AND gate inputs directly while B is inverted by an inverter gate so that it becomes one, or true, at the other AND gate input. We are not finished with the circuit because it would involve the purchase of two types of gates, and that seems wasteful because an inverter gate and an AND gate would be required. Please click on the figure to open it in a new window.

Let’s see if this circuit can be implemented with NAND gates. A NAND gate may be thought of as an AND gate whose output has been inverted. Thus, we can implement Figure 3 with NAND gates as shown in Figure 4. An inverter gate may be created by tying the two inputs of a NAND gate together. As an exercise, try applying all of the A and B inputs in the truth table of Figure 2 to Figure 4 to be convinced that this logic diagram will work. One way of looking at it is to observe that we have a NAND gate that has been inverted. That produces an AND gate. Thus, Figures 3 and 4 are equivalent.

Figure 4. The Logic Diagram Of Figure 3 Implemented With NAND Gates Only. This may be implemented with a single 14-pin dual inline package (DIP) or surface mount package (SMP). The gates come four gates to a package so the extra gate may be used for an extra output or it may be tied high, if unused, to prevent it from toggling. The CD4011 would be ideal for this project because of its wide supply voltage range. Please click on the figure to open it in a new window.

Printed Circuit Board Layout

A printed circuit board layout was completed for a single CD4011 Quad NAND gate on the free, easy-to-use EasyEDA online graphics package [12]. The board is being fabricated by JLCPCB [13] for rapid turnaround.  The schematic diagram is shown in Figure 5. A 3-D rendering is shown in Figure 6. The total board area is approximate 1 square inch, and it will fit nicely onto the corner of the front panel PCB as a mezzanine board. There, it will connect directly to the Arduino MEGA 2560 to perform the lockout function.

Figure 5. Transmit Lockout PCB. The schematic was completed on the easy-to-use EasyEDA online graphics package, as was the Gerber file for PCB fabrication. Please click on the figure to open it in a new window.

.

Figure 6. The CD4011 Quad NAND Gate 3-D PCB Layout. A single CD4011 Quad NAND gate is all that is necessary to implement the transmit lockout during general coverage mode. The screw terminal strips do not appear in the virtual rendering because they were unavailable in the library. Please click on the figure to open it in a new window.

References

[1] New Math, https://en.wikipedia.org/wiki/New_Math

[2] Russell, Bertrand, https://en.wikipedia.org/wiki/Bertrand_Russell

[3] Copi, Irving, Symbolic Logic, 5th ed., Pearson, 1 Jan 2015.

[4] Copi, Irving, https://en.wikipedia.org/wiki/Irving_Copi

[5] Rote Learning, https://en.wikipedia.org/wiki/Rote_learning

[6] Sputnik, https://news.harvard.edu/gazette/story/2007/10/how-sputnik-changed-u-s-education/

[7] Lehrer, Tom, https://en.wikipedia.org/wiki/Tom_Lehrer

[8] Boole, George, https://en.wikipedia.org/wiki/George_Boole

[9] Scott, Rick, N3FJZ, Circuit6040 website, http://www.remmepark.com/circuit6040/

[10] Scott, Rick, N3FJZ, Circuit6040 YouTube Channel, https://www.youtube.com/results?search_query=circuit6040

[11] Scott, Rick, N3FJZ, Circuit6040 YouTube, Module # 110 Front Panel MEGA Quick Start – MAX-SSB Transceiver Project, https://www.youtube.com/watch?v=5a9tlg8SIrk

[12] EasyEDA,  https://easyeda.com/

[13] JLCPCB,  https://JLCPCB.com/

Disclaimers

These circuit designs are provided for informational and educational purposes only and are supplied “as is” and without warranties of any kind, express, implied, or statutory. No representations or warranties are made regarding the accuracy, adequacy, completeness, legality, reliability, or usefulness of this information, either in isolation or in the aggregate. These circuit designs may contain links to or information based on external sources or third-party content. Endorsement and responsibility for the accuracy or reliability of such third-party information or for the content of any linked websites are not taken.

 

 

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IF to Audio Baseband Converters for QRP SSB

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Introduction

Previously [1], an RF to IF Converter was described that precedes this module in a 10-Band QRP Single Sideband (SSB) transceiver.

The IF to Audio Baseband Converter modules described in this paper both serve to convert a 9 MHz Intermediate Frequency (IF) to baseband audio upon receive and from baseband audio to a 9 MHz IF upon transmit. Only one of these modules is required, and an explanation is provided for why two have been designed and built.

The discussion in this paper will be restricted to voice transmission and reception. Digital data transmission and reception on SSB will not be discussed.

Though used in the form of a trigonometric identity in one of the derivations; discussion of the Hilbert transform has been avoided.

Circuit Design

There are circuit commonalities and differences for both circuit boards designed for this application.

Module Commonalities

Please refer to the schematic diagrams in Figures 1 and 2 for this discussion. Both IF to Audio Baseband Converters employ Bridged-T Diplexers [2][3], pi-attenuators [4], and impedance matching transformers [5] on the BFO ports of their Mini-Circuits ADE-1 mixers [6]. Both employ audio diplexers [7] on their mixer IF ports. Both employ a low noise LM723 regulator [8] in a millivolt DC power supply to unbalance a Mini-Circuits ADE-1 mixer used as a balanced modulator for the purpose of reinjecting a carrier into the up-conversion path upon transmit. The carrier is used for antenna tuning. The command to unbalance the balanced modulator is asserted from the Control Panel by depressing the push-to-talk (PTT) button on the MIC or the PTT push-button on the Control Panel once the F1 button on the Control Panel has been pressed to display Tune on the 3.2” TFT display [9].  The Control Panel and TFT display will be described in another article.

One further commonality is the dual-function use of ADE-1 mixers in both module designs. Upon receive, they serve as product detectors for demodulation of the time-dependent audio message. Upon transmit, they serve as balanced modulators to mix the time dependent audio message with the IF carrier frequency for up-conversion. Descriptions of how product detectors and a balanced modulators work are provided in later sections.

Module Differences

Please refer to the schematic diagrams in Figures 1 and 2 for this discussion. The first IF to Audio Baseband Converter module incorporates a Wes Hayward, W7ZOI, fixed gain, bidirectional, termination insensitive amplifier (TIA) [10][11][12] for both transmit and receive paths, while the second incorporates the W7ZOI termination insensitive, closed-loop, IF AGC amplifier [13][14][15] in the receive path, and an open-loop, variable gain, W7ZOI termination insensitive amplifier (TIA) [16][17] in the transmit path. The variable gain amplifier has been implemented with an open-loop, AGC amplifier to which has been added an onboard gain adjustment trimpot. This trimpot is used during module tests. It is removed during transceiver integration and is replaced by a control panel potentiometer that sets the transmitter drive level.

Figure 1. The IF to Audio Baseband Converter Schematic Diagram. This module employs a fixed gain W7ZOI bidirectional, termination insensitive amplifier (TIA) for receive down-conversion from 9 MHz IF to audio baseband and from audio baseband to 9 MHz IF for transmit up-conversion. A low-noise LM723 voltage regulator is part of a millivolt, DC, onboard power supply. Its purpose is to unbalance the ADE-1 balanced modulator so that a carrier may be injected during transmit for antenna tuning.

Figure 2. The IF to Audio Baseband Converter with Receive AGC Schematic Diagram. This module employs a W7ZOI Termination Insensitive Amplifier (TIA) with closed loop AGC for receive down-conversion from 9 MHz IF to audio baseband. A W7ZOI Termination Insensitive Amplifier (TIA) with open loop AGC is used for transmit up-conversion. A low-noise LM723 voltage regulator is part of a millivolt, DC, onboard power supply. Its purpose is to unbalance the ADE-1 balanced modulator so that a carrier may be injected during transmit for antenna tuning.

What is a Balanced Modulator?

In the time domain a SSB signal containing the message is generated by multiplying a time dependent audio message signal by a time dependent IF carrier signal in a mixer used as what is called a balanced modulator. The audio message information is injected into the IF port of the balanced modulator while a local oscillator (LO) signal is injected into the LO port of the balanced modulator. What results is a double sideband suppressed carrier signal in the time domain. There are other methods used to produce SSB signals, but we will limit this discussion to the use of a double balanced mixer for this example. The problem could also be described in the frequency domain, but that solution will not be presented at this time. For sake of example, we neglect higher order, odd harmonics of the LO signal because the LO signal is a square wave. Also, for simplicity, we will neglect the phase terms that accompany each of the signals.

In order to achieve the best possible carrier cancellation in a double balanced mixer used as a balanced modulator, care must be taken to ensure that all of the mixer ports have been terminated in 50-ohms. It is also essential to drive the mixer at its required signal level. Once these requirements have been implemented in the design, the signal leaving the balanced modulator will consist of two sidebands, an upper one and a lower one. The carrier will have been greatly suppressed.

The time dependent, equation for the output of a balanced modulator may be derived from two expressions; the first,

is the time-dependent audio message information that is injected into the IF port of the balanced modulator,

where:

It is important to remember that the time-dependent audio message signal may or may not be a single sinusoidal frequency. For example, voice is quite complex and contains many frequency components. For simplicity here, though, it is defined as a single frequency.

while the second,

is the time-dependent IF carrier signal that is injected into the LO port of the balanced modulator,

where:

For this discussion the assumption is made that the IF carrier signal frequency is much greater than the audio message signal frequency. Multiplying the audio message with the IF carrier, we have for the double sideband suppressed carrier (DSB-SC),

Substituting, we have,

We may recall from trigonometry that the product of two cosines is just,

Substituting, we have,

This equation is comprised of two terms, where the first term,

is called the upper sideband because the output frequency is higher than the carrier.

We know from trigonometry that,

Thus, for the upper sideband, we have,

where the minus sign is correct and is the result of trigonometry.

The second of the two terms is,

which is called the lower sideband because the output frequency is lower than the carrier.

We know from trigonometry that,

Thus, for the lower sideband, we have,

where the plus sign is correct and is the result of trigonometry.

These two sideband equations may be combined in compact form as the double sideband suppressed carrier (DSB-SC) signal,

where the minus sign represents the upper sideband, and the plus sign represents the lower sideband, however counterintuitive it may seem.

One might ask how one of the two sidebands is selected for transmission? The answer comes in the form of a very narrow (of the order of 2.6 kHz wide) crystal bandpass filter [10] centered somewhere near 9 MHz. If upper sideband transmission is desired, that frequency is shifted downward so that the upper sideband sits in the passband of the crystal bandpass filter. If lower sideband transmission is desired, that frequency is shifted upward so that the lower sideband sits in the passband of the crystal bandpass filter. This is accomplished by shifting the LO frequency to the balanced modulator by a few kHz.

All of this requires some a priori knowledge of where the center frequency of the crystal bandpass filter is located. Once known, the audio message information may be shifted so that it is centered in the crystal bandpass filter passband for either sideband.

What is a Product Detector?

In this context a product detector is a demodulator used to recover audio message information from a SSB voice message signal. If a double balanced mixer is used as a product detector, a SSB signal enters the RF port of the mixer while a local oscillator beat frequency oscillator (BFO) signal is injected into the local oscillator (LO) port. When the listener tunes the receiver BFO frequency close to the carrier frequency that was removed prior to SSB transmission, the audio message information becomes intelligible to the listener. This presupposes that the signal is transmitted on upper or lower sideband in accordance with conventions used on the ham bands. It is important that hams work to the same conventions everywhere on the planet or the system will break down.

Product detection may also be described in a few trigonometric equations. This time we use the same double balanced mixer as a product detector. After passing through our crystal bandpass filter, the upper or lower sideband signal is sent to the RF input of the product detector. A BFO signal is injected into the product detector LO port to match the frequency of the carrier that originally generated the SSB transmission. Once tuned to the correct sideband, the output of the product detector passes through a lowpass filter to remove all of the remaining high frequency components, thereby recovering the message audio.

In the previous section it was shown that the DSB-SC signal may be represented by,

This expression contains the message on both of the sidebands, where the carrier has been suppressed.

If we want to recover the voice audio message information, we select the appropriate sideband that has been transmitted based upon the ham band in use.

In order to simplify the expression appearing above without any discussion of the Hilbert transform, let’s make some simple trig substitutions, and we will dispense with any of the constant terms out front. Let’s represent the time-dependent voice audio message in this way,

Furthermore, we can use a trigonometric identity,

Transformations of this type are quite common in communication theory, but we will not dwell upon them.

These two quantities having been defined; we may write our equation for DSB-SC in this way,

Now, suppose that we multiply the preceding expression by the same carrier frequency, presumably in the product detector, and we have for the carrier,

where c(t) is the BFO carrier signal that matches the one suppressed during message transmission.

Then, having performed this operation; we will have recovered the modulating time-dependent voice audio message, where,

and where R(t) represents the recovered, time-dependent message prior to filtering.

Multiplying through, we have,

Again, invoking trigonometric substitutions,

and,

which yield,

This may be rewritten to show the carrier frequency instead of the angular frequency,

The first term contains the time dependent audio message information while the last two terms contain the carrier frequency. The carrier frequency terms may be removed by lowpass filtering after the product detector with an audio diplexer to recover the time-dependent audio message.

Why Two IF to Audio Baseband Converters?

The reason that two discrete IF to Audio Baseband Converters were designed and built is twofold.

First, I wanted to fast-track the SSB radio integration task if trouble was encountered with the IF AGC circuit. This turned out to be fortuitous, and that is exactly what occurred. It took some time to de-bug the circuit.

Second, I wanted to be able to compare receiver performance with, and without, IF AGC. Differences in receiver dynamic range and sensitivity were anticipated.

Construction

Both circuit cards were designed on EasyEDA [18] CAD software that is available for free download and use. PCB fabrication was completed from transmitted Gerber files by JLCPCB [19] in Hong Kong. Turnaround time was 10-days. In order to reduce the number of via holes on the circuit boards, 4-layers were adopted. The top layer consists of ground plane. Vertical SMA RF connectors on the surface of the boards put the ground plane to good use. DC and signal connections to the amplifiers and mixers are made via pin headers and DuPont wires as are visible in Figures 3 and 4. Each of the modules derives its input from a crystal bandpass filter [20] that has sharp skirt selectivity.

Several features are visible on each of the circuit boards:

·        W7ZOI Termination Insensitive Amplifiers (TIAs) in use on both boards to present 50-ohms to the balanced modulator RF port on transmit and the product detector RF port on receive

·        A Mini-Circuits ADE-1 mixer functions as a balanced modulator upon transmit and a product detector upon receive

·        A transformer on the BFO port to transform the impedance level of the SI5351 Clock Generator to 50-ohms

·        A pi-attenuator to adjust the BFO drive level to that required by the mixer

·        An LO diplexer is used to present 50-ohms to the mixer LO port

·        An audio diplexer is used on the mixer IF port to present a 50-ohm load to the IF port, and to filter out any RF appearing on the IF port upon receive so that the audio message may be recovered

·        A low noise LM723 voltage regulator is used in a millivolt power supply configuration so that the balanced modulator may be unbalanced for carrier injection

Figure 3. IF to Audio Baseband Converter without AGC. The IF to Audio Baseband Converter module without AGC consists of a W7ZOI bidirectional, termination insensitive amplifier (TIA) to the left, a Mini-Circuits ADE-1, +7 dBm level mixer at the center, and a millivolt power supply to the right. The mixer serves as a product detector for receive and a balanced modulator for transmit. The relay at the lower right switches 100 mV onto a 50 ohm termination at the IF port of the mixer to unbalance it. This serves to inject a carrier into the transmit path so that the antenna may be tuned to resonance. An audio diplexer is visible on the IF port. This serves to terminate the IF port in 50 ohms while providing a lowpass filter to pass the receiver audio. There is a transformer visible on the LO port of the mixer that serves to match the 76 ohm output impedance of the SI5351 clock generator used as the beat frequency oscillator (BFO) to the 50 ohms required by the LO diplexer and the ADE-1 mixer LO port. A pi-attenuator is provided between the transformer and the diplexer to drop the SI5351 level to +7 dBm.

Figure 4. IF to Audio Baseband Converter with AGC. A W7ZOI termination insensitive amplifier (TIA) is visible to the left. It is used during receive only, and it operates with closed loop AGC. The AGC output voltage also serves as the S-meter signal that is routed to the Arduino S-meter input for display on a 3.2” TFT display. Another W7ZOI termination insensitive amplifier (TIA), set to fixed gain for test, is visible second from the left. It is constructed from an amplifier that has an open loop AGC input. A potentiometer on the AGC port is used to set a fixed transmitter drive level. The Mini-Circuits ADE-1 mixer, second from the right is used as a product detector on receive and a balanced modulator on transmit. The circuitry to the far right generates 100 mV that is applied to the 50 ohm termination on the IF port of the mixer. This serves to inject a carrier into the transmit chain so that the antenna may be tuned to resonance.  The relay in the photo switches the 100 mV onto the 50 ohm termination on the IF port of the mixer. A transformer is visible on the LO port that transforms the 76 ohm output impedance of the SI5351 clock generator to the 50-ohms required on the mixer LO port. A pi-attenuator is located between the transformer and the LO diplexer to lower the signal level to that required by the +7 dBm mixer. An audio diplexer and lowpass filter provides a 50 ohm match to the IF port while allowing only audio to pass.

References

[1] Blustine, Martin, K1FQL, An RF to IF Converter for QRP SSB Transceiver Use, N1FD, 4 August 2025. https://www.n1fd.org/2025/08/04/transverter/

[2] Ibid.

[3] https://www.changpuak.ch/electronics/calc_16a.php

[4] https://leleivre.com/rf_pipad.html

[5] Blustine, Martin, K1FQL, Impedance Matching to an 8-Pole Quasi-Equiripple (QER) Crystal Bandpass Filter, N1FD, 21 May 2024. https://www.n1fd.org/2024/05/21/crystal-filter/

[6] Mini-Circuits, https://www.minicircuits.com/WebStore/dashboard.html?model=ADE-1

[7] Lewallen, Roy, W7EL, An Optimized QRP Transceiver for 7 MHz, ARRL, https://www.arrl.org/files/file/Technology/tis/info/pdf/93hb3037.pdf

[8] Texas Instruments, https://www.ti.com/lit/ds/symlink/lm723.pdf

[9] Adafruit, https://www.adafruit.com/product/1743?srsltid=AfmBOopGfznYc8RKuumddbQzWwXY_d1ByQd07CqiPAZ_xqBDg2jOWuzv

[10] Hayward, Wes, W7ZOI and Kopski, Bob, K3NHI, A Termination Insensitive Amplifier for Bidirectional Transceivers, 26 June 2009. https://w7zoi.net/bidirectional_matched_amplifier.pdf

[11] Land Boards, A Termination Insensitive Amplifier for Bidirectional Transceivers. https://land-boards.com/blwiki/index.php?title=A_Termination_Insensitive_Amplifier_for_Bidirectional_Transceivers

[12] Tindie, A Termination Insensitive Amplifier for Bidirectional Transceivers. https://www.tindie.com/products/land_boards/termination-insensitive-rf-amplifier/

[13] Hayward, Wes, W7ZOI and Damm, Jeff, WA7MLH, The Hybrid Cascode – A General Purpose AGC IF Amplifier, QST, December 2007. https://www.ka7exm.net/hycas/hycas_200712_qst.pdf

[14] Hayward, Wes, W7ZOI, Regarding Circuit Boards for the Hybrid Cascode General Purpose IF AGC Amplifier. https://w7zoi.net/hycas-pcb.html

[15] Carney, Todd, K7TFC, Mostly DIY RF, https://mostlydiyrf.com/hycas/

[16] Hayward, Wes, W7ZOI, Adding AGC to a Termination Insensitive Amplifier, 27 October 2021. https://w7zoi.net/tia+agc.pdf

[17] Carney, Todd, Mostly DIY RF, TIA-AGC RF Amplifier. https://mostlydiyrf.com/tia-agc/

[18] EasyEDA. https://easyeda.com/

[19] JLCPCB. https://jlcpcb.com/?from=VGBNA&utm_source=google&utm_medium=cpc&utm_campaign=13059631621&utm_content=581194145188&utm_term=b_jlcpcb&adgroupid=118955305341&utm_network=g_&gad_source=1&gad_campaignid=13059631621&gclid=EAIaIQobChMIssG71-mZjwMVBjIIBR1NEDo_EAAYASAAEgKrzvD_BwE

[20] Blustine, Martin, K1FQL, Impedance Matching to an 8-Pole Quasi-Equiripple (QER) Crystal Bandpass Filter. Op. cit. https://www.n1fd.org/2024/05/21/crystal-filter/

Disclaimers:

The circuits included on these PCBs were sourced from a number of authors. This is a somewhat advanced and expensive project, and some prior design and construction experience is recommended before taking on a project of this magnitude. These circuit designs are provided for informational and educational purposes only and are supplied “as is” and without warranties of any kind, express, implied, or statutory. No representations or warranties are made regarding the accuracy, adequacy, completeness, legality, reliability, or usefulness of this information, either in isolation or in the aggregate. These circuit designs may contain links to or information based on external sources or third-party content. Endorsement and responsibility for the accuracy or reliability of such third-party information or for the content of any linked websites are not taken.

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An RF to IF Converter for QRP SSB Transceiver Use

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In planning for a homebrew QRP SSB transceiver build, it was decided that all of the amplifiers for RF and IF use would be assembled from kits, or purchased preassembled from any of several suppliers in order to save time and money.

The RF to IF Converter described in this article is a good example of how off-the-shelf parts may be packaged to create a working module

The RF to IF Converter is tuned by an SI5351 Clock Generator VFO over the frequency range of 1.1 MHz to 38.7 MHz. This is the VFO frequency tuning range required for high side and low side LO injection to a mixer for 10-band HF operation.

Subassembly List

Mostly off-the-shelf parts that constitute this module are

·        a W7ZOI termination insensitive (TIA) amplifier with manual gain control for receive down-conversion [1],

·        a W7ZOI termination insensitive (TIA) amplifier with manual gain control for transmit up-conversion [2],

·        a Mini-Circuits ADE-1 mixer for receive down-conversion to IF and transmit up-conversion to RF [3],

·        W7ZOI bi-directional termination insensitive (TIA) RF amplifier pair with fixed gains for post-mixer receive IF preamplification, and for pre-mixer transmit IF preamplification [4],

·        a Bridged-T-Diplexer that provides a 50-ohm termination to the IF port of the ADE-1 mixer [5],

·        a Toroidal transformer that transforms the output impedance of the VFO synthesizer from 76-ohms to 50-ohms (see text), and

·        a VFO attenuator that reduces the VFO synthesizer drive level to that required by the ADE-1 mixer, +7 dBm [6].

Circuit Descriptions

W7ZOI Termination Insensitive Amplifier (TIA) w. Manual Gain Control

The Wes Hayward, W7ZOI, Termination Insensitive Amplifier (TIA) combines a transistor gain stage, a hybrid cascade (HYCAS) adjustable gain stage, and a two-stage buffer into a single amplifier circuit. Two of these amplifiers are in use on this PCB. They are used as the first amplifier in the receiver and the last amplifier in the transmit chain before the power amplifier. Gain control for this amplifier is designed to work between +1 and +4 VDC, but operation is described down to 0 VDC. At maximum gain, +4 VDC, the gain is 31 dB. In his paper, W7ZOI states that 70 dB of gain control should be possible [7]. For a -30 dBm input signal level at maximum gain, the output should be +1 dBm. W7ZOI notes that there is some gain falloff at higher frequencies. Gain controls for these amplifiers are located on the Control Panel (not pictured).

Mini-Circuits ADE-1 Mixer

A doubly balanced mixer, the Mini-Circuits ADE-1 [8], is used as the RF to IF down-converter upon receive, and the IF to RF up-converter upon transmit. This is a medium LO drive mixer that requires +7 dBm to operate with specs. The nominal conversion loss for this mixer is 5 dB.

W7ZOI Bidirectional Termination Insensitive Amplifier

The W7ZOI Bidirectional Termination Insensitive Amplifier (TIA) differs in architecture from that of the TIA with gain control described above. This amplifier consists of three bipolar transistors in the forward direction and three bipolar transistors in the reverse direction [9]. It has been designed to be termination insensitive in either direction. In this application, the amplifier is biased in the forward direction upon receive and in the reverse direction upon transmit. The nominal gain in each direction is 15 dB. The noise figure of each of the amplifiers was reported to be 5.8 dB by W7ZOI. The output third order intercept point (OIP3) was measured to be +20.5 dBm. The 1 dB compression point was estimated to be +3.5 dBm. This is due to low current transistor biasing. While this intercept point may be adequate for QRP operation, this amplifier won’t win any prizes for dynamic range. This provides an opportunity for future improvement.

Bridged-T Diplexer

In order to obtain the best performance from a doubly balanced mixer, it is vital to terminate all of its ports in 50-ohms. In this application, the RF port “sees” a termination insensitive amplifier. The IF port will also see a termination insensitive amplifier (TIA). I chose to include a Bridged-T Diplexer on the IF port in hopes of improving the mixer performance. The Bridged-T Diplexer consists of 9 MHz series and parallel resonant circuits placed between the mixer IF port and the IF TIA.

Referring to the schematic in Figure 1, the series resonant circuit at the IF frequency of 9 MHz appears to be a low impedance, and it increases to a high impedance away from resonance. The parallel resonant circuit appears like a high impedance at the IF frequency. At frequencies away from the IF frequency, the parallel resonant circuit looks like a low impedance. Consequently, the 50-ohm resistor, R1, to the left, appears across the mixer IF port for frequencies away from the IF frequency. Similarly, for frequencies far from the IF frequency, the TIA amplifier that follows sees the 50-ohm resistor, R2, to the right.

Figure 1. The Bridged-T Diplexer. The series resonant circuit at the IF frequency of 9 MHz appears to be a low impedance, and it increases to a high impedance away from resonance. The parallel resonant circuit appears like a high impedance at the IF frequency. At frequencies away from the IF frequency, the parallel resonant circuit looks like a low impedance. Consequently, the 50-ohm resistor, R1, to the left, appears across the mixer IF port for frequencies away from the IF frequency. Similarly, for frequencies far from the IF frequency, the TIA amplifier that follows sees the 50-ohm resistor, R2, to the right. Please click on the figure to open it in a new window.

In order to design a diplexer of this type, a circuit Q must be specified. Some designs use different Q values for the series and parallel resonant circuits. For this design, Q = 10 was chosen to be the same for both. An online calculator was used to design this Bridged-T Diplexer [10].

VFO Impedance Matching Transformer

It has been determined by direct measurement that the output impedance for an SI5351 synthesizer is not 50-ohms. (The SI5351 Clock Generator output power level and impedance measurement is the subject of a future article.) The measured output impedance does not match the data sheet [11] impedance of 85-ohms at 8 mA bias current. It has been shown that the impedance is closer to 76-ohms at a measurement frequency of 10 MHz, at least for the SI5351 in use. Consequently, the impedance ratio was found to be 1.52:1.

In order to ensure the best possible match, a broadband transformer should be used to perform the impedance transformation if possible. An L-matching network won’t work because the VFO requires a broadband match. Once an FT37-43 toroid core was chosen, the turns-ratio was calculated by taking the square root of the impedance ratio, 1.52:1, resulting in a turns-ratio of 1.233:1. Next, the primary and secondary turns numbers were determined that were as close to whole numbers as possible with the constraint that the winding having the fewest number of turns have an impedance of at least 50-ohms x 5 = 250-ohms.

The turns-ratio that closely matches the requirement is 16T:13T. Dividing the two, obtains 1.231:1. When squared, a value of 1.515:1 is obtained, which is close to the original impedance ratio of 1.52:1.

Next, the impedance of the smaller of the two windings, 13 turns, was checked at the lowest VFO frequency of operation. This is 1.1 MHz for the 30m band. For this verification, a hand calculation can be performed, as has been done in the past, or an online calculator can be used [12]. The result was found to be 409-ohms > 250-ohms, so this winding meets the impedance criterion. Further measurements are required to ascertain that there are no resonances for this transformer over the entire VFO tuning range. Should in-band resonances be encountered, the transformer will be discarded.

A turns-ratio of 11T:9T might also work, but it is not as close a match to the original impedance ratio of 1.52:1. Please check this turns-ratio calculation as an exercise. Also, for practice, please check the 9T winding against the 250-ohm impedance criterion at 1.1 MHz to see if it meets it. Please let me know in the comments section.

VFO Attenuator

The signal output of the SI5351 Clock Generator used to provide the LO to the mixer was calculated and measured to be +11.48 dBm. This would suggest that a ~ 4 dB pad should be used at the mixer LO port input to obtain ~ +7 dBm. If a resistive pad in the PI-configuration is used, the resistor values may be calculated by hand, or an online calculator may be employed [13]. The ~ 4 dB attenuator in Figure 2 uses standard resistor values.

Figure 2. A 4 dB PI-Attenuator. This attenuator uses standard resistor values. They are close enough for this application, where no precision is required. Please click on the figure to open it in a new window.

Schematic Diagram

The schematic diagram of the RF to IF Converter is shown in Figure 3. A pair of manual gain controls (not shown) is provided on the Control Panel. Upon receive, the manual gain control will alter the dynamic range and the receiver noise figure. Upon transmit, the manual gain control will alter the transmitter drive level.

Figure 3. RF to IF Converter Schematic Diagram. This circuit provides RF to IF down-conversion on receive and IF to RF up-conversion on transmit. Manual gain controls are accessible from the Control Panel (not shown). The receive gain control will alter the dynamic range and noise figure upon receive. The transmit gain control will alter the amount of output power upon transmit. Please click on the schematic to open it in a new window.

Printed Circuit Board Layout

The printed circuit board layout is shown in Figure 4. Two minor labeling corrections to the PCB are visible since the silkscreen labeling was interchanged. A coupling capacitor, C10, was added to the PCB at the transformer, T1, input. The transformer must be AC-coupled to the SI5351 Clock Generator.

Figure 4. RF to IF Converter PCB. Two W7ZOI Termination Insensitive Amplifiers (TIA’s) with gain control, a Mini-Circuits ADE-1 Doubly Balanced Mixer, and a W7ZOI Bidirectional Termination Insensitive Amplifier (TIA) provide RF gain control and conversion to a 9 MHz IF on receive and from 9 MHz IF to RF on transmit. A Bridged-T Diplexer tuned to 9 MHz provides a constant 50-ohm termination at the IF port of the mixer. Please click on the photo to open it in a new window.

References

[1] Carney, Todd, K7TFC, Mostly DIY RF. https://mostlydiyrf.com/tia-agc/, and https://mostlydiyrf.com/wp-content/uploads/2023/12/TIA-AGC_manual.pdf, and https://w7zoi.net/tia+agc.pdf

[2] Ibid.

[3] CalOutlet. https://www.ebay.com/itm/135758562145?itmmeta=01K1GR7N4T7T8MPD3QGCY00E4T&hash=item1f9bd74361:g:IzMAAOSwxVVoFn7M

[4] Land-Boards, LLC. https://www.tindie.com/products/land_boards/termination-insensitive-rf-amplifier/, and https://w7zoi.net/bidirectional_matched_amplifier.pdf

[5] Bridged-T Diplexer Calculator. https://www.changpuak.ch/electronics/calc_16a.php

[6] PI-Attenuator Design Calculator. https://leleivre.com/rf_pipad.html

[7] Hayward, Wes, W7ZOI. https://w7zoi.net/tia+agc.pdf

[8] Mini-Circuits ADE-1 mixer. https://www.minicircuits.com/pdfs/ADE-1.pdf?srsltid=AfmBOorxmabfezmF18FfPBt4-gGTfS8pEvwuLJuSS6lKZoLp0jG9YTk1

[9] Wes Hayward, W7ZOI. https://w7zoi.net/bidirectional_matched_amplifier.pdf

[10] Bridged-T Diplexer Calculator, Op. cit. https://www.changpuak.ch/electronics/calc_16a.php

[11] Silicon Labs Data Sheet, p. 4. https://cdn-shop.adafruit.com/datasheets/Si5351.pdf

[12] Toroidal Inductor Calculator. https://toroids.info/FT37-43.php

[13] PI-Attenuator Design Calculator, Op. cit. https://leleivre.com/rf_pipad.html

Disclaimers:

The circuits included on this PCB were sourced from a number of authors. Only the 4-channel MUX decoder is original work. This is a somewhat advanced and expensive project, and some prior design and construction experience is recommended before taking on a project of this magnitude. This circuit design is provided for informational and educational purposes only and is supplied “as is” and without warranties of any kind, express, implied, or statutory. No representations or warranties are made regarding the accuracy, adequacy, completeness, legality, reliability, or usefulness of this information, either in isolation or in the aggregate. This circuit design may contain links to or information based on external sources or third-party content. Endorsement and responsibility for the accuracy or reliability of such third-party information or for the content of any linked websites are not taken.

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