Here we will examine a popular function generator’s (Figure 1) behaviour and performance when one its outputs is connected to a low-resistance load. This information is important for circuit designers, when selecting the applications for this circuit.

The setup

The selected circuit consists of three op-amps, each being able to generate rectangular, triangular and sinusoidal signals.

Figure 2 shows the signals when the circuit’s outputs are not connected to a load; as you can see, all signals look stable.

Figure 1: A popular function generator circuit

Figure 2: Function generator signals when none of the outputs are connected to a load

The circuit’s power is kept fixed at +5Vdc and -5Vdc. A variable load resistor is connected to each output, to examine the stability of the circuit’s outputs at any given scenario.

The resistor is first connected to the rectangular output, with the signal shapes monitored when the resistor’s value reduces. The same steps are repeated with the load resistor connected to the triangular and sinusoidal signal outputs.

Scenario 1: Loading the rectangular output

By plotting the circuit signals’ peak-to-peak values at various load resistances on the rectangular output, the circuit delivered stable outputs for the rectangular, triangular and sinusoidal signals, when the load resistance is over 254 Ohms. Below this value, all signals start to rapidly deteriorate; see Figure 3.

Figure 3: Signal behaviour when a load resistor is connected to the circuit’s rectangular output

Scenario 2: Loading the triangular output

When the load resistor is connected to the triangular signal output, the circuit shows a very stable rectangular signal. However, the triangular and sinusoidal output signals deteriorate rapidly for load resistances below 130 Oms; see Figure 4. Still, this circuit shows better performance in this setup compared with scenario 1.

Figure 4: Signal behaviour when a load resistor is connected to the circuit’s triangular output

Scenario 3: Loading the sinusoidal output

When the load resistor is connected to the sinusoidal signal output, the circuit shows a very stable behaviour at both the rectangular and triangular signal outputs. However, only the sinusoidal output signals deteriorate rapidly for load resistances below 132 Oms. The circuit shows better performance in Scenario 3 compared with Scenarios 1 and 2; see Figure 5.

Figure 5: Signal behaviour when a load resistor is connected to the circuit’s sinusoidal output

Hence, results show that the function generator circuit is not providing ideal performance when load resistance drops below a certain level (threshold resistance). This threshold resistance is not even the same with each output signal. This clearly indicates that loading one output of the circuit will impact the other outputs, and that some applications call for more robust and complex function generator circuits, to operate outside the operating windows defined in this experiment.

By Sulaiman Algharbi Alsayed, Managing Director, Smart PCB Solutions

When Ian Darney was a student apprentice, he constructed his first valve radio. His colleagues advised him to drill a hole in the chassis, fit a solder tag, and connect all the return conductors to that terminal. The radio worked OK. But there was a constant hum from the speaker, due to interference cause by the 50Hz supply to the valve heaters.

After graduating, he spent his working life at British Aerospace. One project was the design of a ground trainer for the Martel missile. This had a TV camera in the nose. The simulator consisted of a flying spot scanner with a trapezoidal raster which illuminated a film which had been created by a high flying aircraft. A lens on the other side focussed the light onto a photomultiplier and the video output displayed on a TV screen. This simulated the view that would be seen by the missile controller. It worked OK. However, the contractor insisted on the use of a single-point ground; a terminal on the equipment rack to which power, analogue signals, and digital signals were grounded. The system worked OK, but suffered from every interference problem imaginable.

Later on, he was a member of the team who built the Photon Detector Assembly (The heart of the Hubble Space Telescope). He designed Partial Discharge test equipment for the high voltage supplies to the Camera and Image Intensifier. This could detect a one micro-amp pulse of current of one micro-second duration (1pc). This worked well in the Vacuum Test Facility. But when the test equipment was moved to the Spacecraft Assembly Area, it was swamped by the noise from the power supply system.

When the Space Systems Division folded, Ian transferred to the Airbus Division and became the Bristol representative on the Eurocae working group which defined requirements for the protection of aircraft from the effects of lightning. He had many interesting discussions with engineers from other European countries, with scientists from the Lightning Test Facility at Culham Laboratories, and with representatives from the RTCA; the organisation that defines requirements for aircraft in the USA.

It was apparent that the concepts of the ‘Single-point Ground’, the ‘Equipotential Ground’ and the corollary ‘avoid Earth Loops’ had become accepted wisdom in the Engineering community. These concepts are false. They are the prime cause of the vast majority of interference problems.

After retirement, he set up a room in his house and carried out experiments on Electromagnetic Interference. This necessitated re-reading old books of lecture notes which had been copied from a blackboard at Glasgow University, studying books on Electromagnetic Theory, and browsing articles in the Electronics World. He discovered that the false concepts had been endorsed by the writers of several popular books on EMC.

This provided enough material to write the book ‘Circuit Modeling for Electromagnetic Compatibility. Its purpose was to justify a set of guidelines which could replace the false concepts underlying the ‘Grounding Philosophy’ used in the design of aircraft, spacecraft and vehicles. 

After the book had been published, he produced a couple of papers. The research involved in creating these documents has led to an improved understanding of the mechanisms involved in the propagation of electromagnetic interference (EMI). Because they had also been subject to critical review, they provided confidence in the reliability of the reasoning.

Circuit Theory is a development and simplification of Electromagnetic Theory. It provides the analytical tools necessary to simulate the functional performance of complex printed circuit boards, as well as electrical machinery. But the simplifications introduced during its initial development prevent its use in the analysis of EMI.

Electromagnetic Theory provides all the formulae needed to analyse EMI, since it deals with the relationships between the electromagnetic field and the behaviour of conductors. It is possible to incorporate a few more of these relationships into the toolset of Circuit Theory; just enough to enable it to simulate the mechanisms involved in the propagation of EMI.

Circuit Theory can be updated to simulate EMI coupling without compromising its ability to simulate functional performance. The starting point is the replacement of the ‘equipotential ground’ with two conductors. A three-conductor assembly can simulate the cross coupling between two separate loops.

Over the past three years, further research led to the creation of  a set of articles on the topic of ‘Updating Circuit Theory’. These have been uploaded to the ‘Web Exclusive’ section of the Electronic World website.

It is hoped that readers of EW will find some of the ideas useful in the design of new equipment. In particular, the articles on power supply distribution contain new ideas about the design of Power Line Filters. In general, the description of the mechanisms involved in the propagation of EMI should lead to better understanding of the phenomenon. One of the most recent articles identifies the relationship between photons and charges.

It is planned to compile these articles into a new book; ‘Updating Circuit Theory’. Its purpose will be to show how circuit models can be used to analyse EMC during the creation of a new product; from the Feasibility Study, through the Prototype and Engineering models, to the final Manufacturing stage. That is, EMC requirements can be treated in exactly the same way as any other design requirement.

Six of the articles have already been compiled into a single document ‘Cross-Coupling Models’; the second chapter of the book. This can be downloaded from www.designemc.info/UCT2.pdf 

It is likely that engineers who have based the design of cable assemblies on the concepts of Grounding Philosophy will have serious doubts about the viability of this new approach. The best way of resolving differences would be to submit comments which could be posted on the EW website. It is also possible to use the Contact page at www.designemc.info

In Memoriam

It is with greatest sadness we report that Ian Darney passed away on the 26th of December, 2021.

We at Electronics World worked with Ian for decades, reporting on his experimental findings related to electromagnetic interference.

The engineering and scientific community has lost a great contributor – a researcher and a thinker – and we at Electronics World miss him tremendously!

Rest in peace, Ian!

Q:        What does “sustainability” mean to you? We hear that word a lot, but we want to understand how you define it.

A:        Sustainability is not a new topic, and there is a mounting awareness that the destructive patterns that we’ve built have resulted in a crisis. Working towards a more inclusive and sustainable world requires us all to rethink how we live our lives and how we can co-create a liveable future. It may seem like a daunting challenge, but I see it as an exciting opportunity. We all have an opportunity to change and rebuild economies and societies that are much more sustainable, and it feels like the political will to support this change is growing.

Q:       What are your ambitions for TT Electronics through this appointment?

A:        I feel lucky to work for a company whose purpose is to solve technology challenges for a sustainable world. This purpose drives our business decisions. Sustainability is central to what we make for our customers – products that are cleaner, smarter and healthier. Sustainability is also central to the way we run our business. We aspire to deliver “zero harm” and minimise our impact on the environment to benefit our stakeholders, including customers and suppliers, employees, communities and shareholders.

We have a strong culture at TT to provide an inclusive and sustainable workplace, and we have clear targets around some initial environmental priorities, including reducing carbon emissions, waste to landfill and single-use plastic packaging.

Sustainability is a broad area, and we will continue to build our agenda, but, overall, we’re focused on doing the right thing, championing the expertise of our talented workforce, and achieving more by working together. That gives me great confidence in our ability to address the sustainability challenges that lie ahead.

Q:       How is TT Electronics likely to implement these ideas into practice and how easy/difficult will that be?

A:        Our purpose is to solve technology challenges for a sustainable world, so it really is at the heart of everything we do. TT engineers advanced electronics that benefit our planet and its people for future generations. We apply this same expertise and enthusiasm from our engaged and passionate workforce to how we operate as a business.

The way in which we do business, working with our customers to design and manufacture solutions that enable a cleaner, smarter and healthier world means contributing to a sustainable world is already part of our DNA. Last year we invested £11.2m in research and development, which was almost entirely focused on making new, lighter products that will make cleaner, smarter solutions and improve wellbeing.

Like every business, we need to challenge how we operate and implement changes to make our business more sustainable. We believe this is an ambition shared by our customers and suppliers. We’re building a clearly defined roadmap and looking to leverage expertise and technology innovation to help us succeed.

Q:       Within what timeframe will these plans be integrated?

A:        I anticipate that our sustainability ambitions will grow and grow. Because of this, I don’t think there will be a point in time when we can say our sustainability ambitions have been completed.

Q:       When did TT introduce its Sustainability Council and what is its remit?

A:        We have a longstanding Health, Safety and Environmental Council responsible for companywide best-practice sharing, monitoring and improvements and strategy setting. This year, we introduced a group-wide sustainability council to focus on developing and integrating our sustainability roadmap.

Q:       Has TT Electronics allocated certain funds towards achieving its ‘green’ goals and to what value – please specify?

A:        We recognise that the roadmap to net-zero emissions in our own operations will require investment. We assess the investment necessary based on return on investment and cost per CO₂ reduction.

It’s worth noting that sustainability is also a driver of revenue and profit growth for TT. We see the demand for our products and services that enable a more sustainable world increasing over time as this continues to be a worldwide prerogative.

Q:        What should “sustainability” mean to electronics as an industry?

A:        The electronics industry is renowned for its innovative approach to technology development and operational excellence in its manufacturing. We need to apply these core competencies to the industry-wide approach to sustainability and the circular economy. Electronics can and should be an excellent enabler for sustainability, so it’s a big opportunity for the industry.

Q:       How can an everyday engineer think of sustainability when dealing with daily projects – whether at the design or implementation stage of components/systems?

A:        Our talented engineering community is one of the greatest assets we have to drive sustainability ambitions through the electronics supply chain. Be it at the new product introduction stage or through process engineering as that product is manufactured, there are opportunities for engineers to identify and develop more efficient and less resource-intensive solutions, which then permeate throughout the value chain. Education and awareness are key to making sustainability considerations part of everyday thinking for all of us to take responsibility for our part in driving the sustainability agenda.

Q:       Does TT Electronics actively encourage its customers to be “sustainable” and how?

A:        We work in strategic partnerships with our customers, and therefore the conversation works both ways. Our customers want to work with us to support their sustainability agendas, and we want to work with them to drive sustainability.

Q:       Are TT Electronics’s customers asking for sustainable products?

A:        Absolutely! But this is nothing new.

Our cleaner solutions improve energy efficiency, addressing climate change and resource scarcity. These solutions include power controls for aerospace and defence markets which contribute to lighter and more environmentally-friendly aircraft, reducing fuel consumption. For example, it has been estimated that a 1% reduction in the weight of an aircraft leads to a c.0.75% improvement in fuel consumption. Our products also contribute to increased aviation safety. As part of the ‘Clean Sky’ initiative and associated economic benefits from increased fuel efficiency, demand for our products in these areas has been growing.
Our smarter solutions ensure accuracy and drive automation, improving productivity and addressing resource scarcity. These solutions include multiple sensors that can be used to improve productivity, including the smarter home and factory. This sensor technology can improve efficiency and therefore reduces energy consumption, resulting in a lower carbon footprint.

We are expert specialists obsessed with solving our customers’ complex problems, so we’re always up for the challenge – working with our customers to help them with their sustainability quandaries.

Q:       What else might we need as a society to see major changes in terms of sustainability and “green-ness”?

A:        Education, education, education! This is fundamental to the growing recognition that we can’t continue on the path the world is currently. As individuals, from world leaders to business leaders, to  other members of society, all of us need to take responsibility for our own influence and impact.

By Svetlana Josifovska, Editor

Circuit Theory provides all the analytical tools necessary to predict the behaviour of any electronic circuit. Central to teaching on this theory is the concept of the ‘Equipotential Ground’. Invoking this concept prevents any attempt to use any circuit network to analyse Electromagnetic Interference.

A review of the relationship of Circuit Theory with Electromagnetic Theory identifies a way of augmenting these analytical tools, and this enables circuit models to be developed to simulate all forms of EMI.

Details of how this objective can be achieved are provided by a set of articles already available at the Electronics World website. They are in PDF format and can be reviewed by entering ‘ Updating Circuit Theory ’ in the EW search panel. This article describes the approach adopted.

Background

All the mechanisms involved in the propagation of Electromagnetic Interference (EMI) are defined by the relationships derived in Electromagnetic Theory. Circuit theory is a development and simplification of the mathematics involved in the derivation process. It has proved to be a reliable and accurate method of designing Electrical and Electronic systems. Over the past century, Circuit Theory has provided all the analytical tools necessary to predict the functional behaviour of these systems. Even so, the unwanted coupling associated with EMI has become increasingly troublesome, to such an extent that it became necessary to develop regulatory requirements to ensure different systems do not interfere with each other.

It is impossible to avoid some level of electromagnetic coupling. So the requirements for Electromagnetic Compatibility (EMC) have been formulated in a way which ensures that the level of interference of the equipment-under-review is within acceptable limits. At the end of the manufacturing process, the equipment is subjected to a series of defined tests in an EMC Test House. If it passes the tests, then it can be claimed that the equipment has meet a defined set of formal regulations. These regulations can then be included in the specification which defines the performance of the equipment.

A whole industry has developed to provide advice and guidelines to equipment manufacturers as to how to design and develop their product in a way which ensures that it has a good chance of meeting the formal EMC requirements. But if the equipment fails to meet these requirements, the consultants will have long gone.

Assessment

As yet, there is no universally accepted method of designing electronic equipment to meet the formal EMC requirements. This is due to several factors.

The mathematics required to analyse the behaviour of three dimensional electromagnetic fields is very complicated. When the author was a student of Electrical Engineering in Glasgow in the late 1950s, he never even heard of the operations ‘div’, ‘del’, and ‘curl’, let alone how to manipulate them. He learnt of the existence of the Maxwell Equations several years later when he was talking to a colleague at British Aerospace. The professors who set the curriculum he followed at university probably decided that the manipulations of such concepts were well beyond the ability of the average student.

The complexity of electronic systems in vehicles, aircraft, spacecraft and ships has created the development of various specialities. Each speciality creates its own jargon and abbreviations. It is often the case that one specialist has difficulty in understanding the reasoning of another specialist. Many abbreviations mean different things to different people.

An almost impenetrable barrier to the Electronic System Designer who hopes to glean information on the topic is the language and jargon of any paper on Computational Electromagnetics.

The problem and the solution can both be found in the analytical tools of Circuit Theory: a theory which is dramatically easier to understand.

Problem

Circuit Theory is a development and simplification of Electromagnetic Theory. As far as EMC is concerned, it contains a simplification too far. This simplification is the concept of the zero-volt ground-plane, represented as a ‘ground’ symbol or an ‘earth’ symbol on circuit diagrams.

SPICE analysis uses this concept to good effect, by calculating the voltage on every node of the network with respect to a single node at which the voltage is defined as zero.  Such a representation allows components such as resistors, inductors, capacitors, diodes and transistors to be mounted on a circuit board and represented as a circuit in which there is one-to-one correlation between the symbol on the diagram and the component on the board. This allows extremely complex assemblies to be analysed. But, by its very nature, it cannot simulate EMI.

Circuit Theory has proved to be so useful and so reliable that many engineers have been led to believe that its rules are the Laws of Physics. In attempting to correlate these rules with the observed phenomenon of EMI, a whole new philosophy has been developed; ‘Grounding Philosophy’. This concept has been endorsed by several eminent researchers. Many authors have integrated this approach into books on EMC. The inclusion of many and varied relationships of Electromagnetic Theory (all of which are undisputable) in these books lends credibility to this false philosophy.

It has been recommended that a terminal be installed on the conducting structure and that all the return conductors of a subsystem be connected to that terminal. That is, all voltages in the subsystem can be referred to this zero-volt terminal. There are signal grounds, logic grounds, power grounds, and many other variations on the theme. Some engineers have advocated such a system with fervour worthy of any religious zealot.

Any system using these guidelines to define the design requirements for any system can be guaranteed to cause problems. These can be inconsequential, annoying, dangerous, or mission critical. The consequences can also be lethal, as with the in-flight breakup over the Atlantic Ocean of Trans World Airlines Flight 800. Figure 46 of the report https://www.ntsb.gov/investigations/AccidentReports/Reports/AAR0003.pdf  clearly shows that the wiring of the fuel system is based on the concept of the single point ground.

Solution

Any link carrying signals or power between two electronic units mounted on a conducting structure is carried by three conductors; the send conductor, the return conductor, and the structure. In this representation, the ‘structure’ represents the effect of every other conductor in the system.

A single conductor can be represented as a T-network with inductors and resistors in the horizontal branches and a capacitor in the vertical branch. Three conductors in parallel are represented as a Triple-T network with the capacitors connected together at a single point. This point represents a location in the far distance where the energy level of the electromagnetic field is zero. Such a representation is closer to reality, where the energy is carried by photons propagating back and forth between the conductors; that is, carried by the electromagnetic field.

Any electronic system can be represented as a block diagram, where the contents of each block define the function of that block and the lines between blocks represent the signals transmitted between them. Instead of focussing attention on the contents of any block, the EMC analysis could treat each link as a separate entity.

The conductors of any signal link can be represented as a Triple-T network. By adding the interface circuitry of the blocks at each end, the cross-coupling between the signal loop and the common-mode loop can be analysed. The effect of an external electromagnetic field can be simulated by adding a voltage source in series with the structure.

By treating each signal link as a separate entity, the analysis of the EMC of the system can be broken down into a number of discrete problems, each of which can be analysed using the tools of Circuit Theory. The technique can be extended to simulate all the mechanisms associated with EMI coupling; Conducted Emission, Conducted Susceptibility, Radiated Emission and Radiation Susceptibility.

Mesh Analysis

The nature of the relationship between the two theories makes it natural to use Loop Equations to analyse the behaviour of the signal link.

When a voltage is applied between two conductors, current flows down the send conductor, creating an electromagnetic (EM) field. This propagates outwards at the speed of light and is reflected by the return conductor. This field arrives back at the send conductor and induces a voltage which enhances the forward current flow. Positive feedback ensures that current flow in the return conductor is in the opposite direction to that in the send conductor. The driving force is the EM field.

This mechanism is basic to both frequency analysis and transient analysis.

Approach

Since this approach involved the development of circuit models which could not be found in the literature on EMC, the only way of checking the accuracy of the simulation was to set up a bench test, record the results, and then compare those results with the model. Puzzling over any deviation between test results and the simulation involved opening old textbooks on electromagnetic theory and relating that theory to the model. New experiments could be devised in the process repeated.

Since the accuracy of each new model could be checked by comparing it with the actual performance of the hardware, and since the construction of that model was derived from the relationships of Electromagnetic Theory, sufficient confidence was acquired to proceed to the next stage.

This is the pattern followed in this series of articles.

It was necessary to develop a set of equations for each model and to create a program which solved those equations. Mathcad software was used for this purpose since these was no need to translate these equations into machine language. Each equation could be copied onto the worksheet in the same form that it was derived.

To enhance understanding of the process, as well as to confirm the validity of the computation used to create response curves, every worksheet is replicated as a Figure in the text. A significant feature of Mathcad is that the test results can be included in the worksheet, allowing test and model results to be displayed on a single graph. Every definition and every computation is visible on the same worksheet. Errors are not difficult to loacate.

This approach means that each article can carry theory, details of a test setup, the test procedure, analysis, computation, correlation, and the assessment. This is different from that covered in traditional textbooks where the theory is introduced step-by-step. Each article in this series is self-standing. This allows the set of articles to be treated as a handbook.

Frequency Analysis

An experiment is described which compares the frequency response of a signal link with that of a Triple-T model. The two responses correlate closely over a range which includes that of full-wave resonance. This demonstrates the reliability of the model.

Any conducting surface of any cross-section can be simulated as an array of parallel conductors in which the current in any conductor will induce a voltage in every other conductor. By treating the array as a set of three composite conductors, a Triple-T model can be constructed of any cable assembly of any cross section. It is shown that a shield does not behave as a barrier to electromagnetic fields; it acts to neutralise the effect of those fields.

A dipole antenna can be represented as a series LCR circuit in which the resistor simulates the effect of the environment. With a two-conductor cable, the environment is represented as a virtual conductor.

With EMC analysis, it necessary to demonstrate that the radiated emission from the assembly-under-review is less than a defined limit and that the assembly is not susceptible to an external field of defined intensity. That is, worst-case conditions are assumed. It transpires that the equations for worst-case conditions are relatively simple. The magnetic field at a distance is proportional to the current in the structure multiplied by the distance. The voltage induced in a conductor is proportional to the strength of the threat field and the length of the conductor.

An example is provided of the method of analysing the susceptibility of a twin-conductor cable used to initiate an electro-explosive device. It goes on to show how to design a simple filter which ensures that the system is safe in the presence of the threat field.

The screens of coaxial cable normally consist of multiple strands of copper wire twisted round the solid central core in a braided pattern.  This means that the length of any conductor of the shield is significantly longer than the core. Since charges are constrained to flow along conductors, the effect can be visualised as an extra length of conductor routed alongside the core. This extra conductor possesses the properties of inductance and capacitance. A test is described which provides data on the frequency responses of the admittance and the transfer admittance. A circuit model is created which replicates that response.  

Transient Analysis

Transmission Line Theory shows that any line can be defined in terms of its characteristic impedance and the time it takes a signal to traverse its length. If it is assumed that there are no losses, then that impedance can be defined as a resistance. A shift register can be used to simulate the time delay. Reflections at each termination are defined by the reflection equations. A program can be created to simulate the transient response of a twin-conductor cable, whatever the interface circuity.

With power supplies, it is not possible to avoid reflections, and these transients are the greatest cause of radiated emissions. The only way of reducing the level of these emissions is to absorb the unwanted energy in resistors. The design of a simple power line filter which absorbs transient energy is described.

This filter is significantly different from conventional filters which protect the load by sending unwanted energy back towards the source. The only place for that energy to go is into the environment; where it re-appears as unwanted radiation.

A circuit model is described which simulates the transient response of a signal link. This caters for the fact that the common-mode current propagates at a higher velocity than the differential-mode current.

Power supplies on aircraft use the conducting structure as a return conductor. It is reasoned that the inclusion of a return conductor would increase the weight of the wiring. Weight is a significant factor in the design of aircraft and spacecraft. However, if a small diameter conductor was routed alongside the send conductor and connected to structure at both ends, this would carry all the high-frequency components, without compromising the ability of the structure to carry the low frequency energy. A review of this effect could form part of a cost-benefit analysis.

A method of matching interface circuitry to the signal link is described. This minimises reflections in both the differential-mode and common-mode loops.

Ground bounce is due to the energy stored in the cables being released into the environment when power is disconnected. An experiment is used to illustrate this phenomenon.

An experiment is described which identifies the relationship between charges and photons. The energy required to emit photons from the surface of a conductor is equal to the energy needed to decelerate the charges which arrive radially at that surface.

Conclusion

The technique described in this set of articles can be used to analyse all the mechanisms involved in the propagation of EMI. This approach avoids the need for endless debate on the topic of ‘Ground Philosophy’. Equally, it avoids the need to invoke the complexities of Electromagnetic Computation.

[Image: Louis Reed for Unsplash]

Many integrated circuits (ICs) still need both positive and negative voltage supplies (i.e., +VCC and -VCC). To obtain these, there are several options, including: using two batteries connected in series (Figure 1), and using a negative voltage supply generator circuit.

Option 1 is expensive as two batteries are required instead of one, but it also adds to the circuit’s size and weight, which is not a preferable option.

Option 2 circuits generate a negative voltage at their output when a positive voltage is applied to their input. Many electronic circuit designers prefer this option since it eliminates the need for a second battery set, it weighs less, it’s smaller and cheaper.

Several circuits can be used to generate negative voltage; however, the simplest, cheapest and lightest is the Schmitt-trigger inverter circuit, which can effectively serve as a negative voltage supply generator.

The circuit in Figure 2 is the perfect choice for generating negative voltage supply in small and low-cost circuits. However, the generated negative voltage supply ranges from -0.1V to 4.8V, depending on C1 and R1 values. Hence, our challenge is to select the best C1 and R1 values to obtain the maximum negative voltage at this circuit’s output.

Figure 1: Two batteries connected to generate negative voltage

Figure 2: Schmitt-trigger inverter circuit connected to generate negative voltage

Methodology

To maximise the generated negative voltage from the circuit in Figure 2, it is very important to understand its operation. Section 1 is a simple oscillator, with the rest mostly used to rectify the signal and charge capacitor C3 with a negative voltage (the output).

Our main challenge is to select C1 and R1 sizes where section 1 generates the maximum oscillation magnitude. The higher the oscillation, the more negative voltage the circuit can generate.

Since the signal shape is not important for our application, we can ignore the distortion of the oscillation circuit.

The magnitude of the signal generated in section 1 is measured with various C1 and R1 components. All C1 and R1 values were changed, and with value set, the oscillation signals (in section 1) were measured, and the best R1 and C1 values for a maximum oscillation signal identified.

Assumptions

• Throughout this experiment, 100 Ohms up to 100k Ohms were used for R1.
• Similarly, the C1 values used were between 1nF and 500nF.
• Capacitors C2 and C3 were set at 100nF and 300nF, respectively.
• Diodes D1 and D2 were selected to be 1N4001, which is a general-purpose diode.

Impacts

Figure 3 shows the oscillation signals for various C1 and R1 values, with the red trace applying to signals below 5V, yellow for signals of 5V, orange for signals between 5V and 5.4V, and green for signals above 5.4V.

Figure 3: Oscillation signal magnitude profile for various C1 and R1 values

From the figure it can be clearly seen that the maximum oscillation signal magnitude (5.44V) is at C1 = 5nF and R1 = 78k or 79k. Consequently, the circuit can generate a negative output voltage of 4.73V, which is its maximum.

A definitive relationship is established between photons and charges. Charges flow axially along the send conductor and radially towards the surface. At the surface, they are stopped by atomic forces. Photons are emitted. The rate of change of the number of departing photons is proportional to the number of charges arriving at the surface. The energy lost to the conductor is measured by the voltage developed along the inductance. The energy stored in the conductor is measured by the number of charges held at the surface. This assessment was obtained by successive refinements of the transmission line model of the differential-mode current waveform in a twin-conductor cable which is open-circuit at the far end.

Introduction

A test is described where a step voltage is applied to the near end of a twin conductor cable which is open-circuit at the far end and a photographic record is taken of the differential-mode current. Then a circuit model is created which replicates the recorded waveform. Analysis of the model provides an insight into the mechanisms involved.

Details are provided of the setup, the test method, and the test result; a waveform with multiple discontinuities. Then a circuit model is created to replicate that waveform. Details are provided of the reasoning used to create that model. A Mathcad worksheet is developed to simulate the recorded waveform. Details are provided of the values assigned to the constants and all the variables are defined. The purpose of each function (subroutine) is described and a block diagram provided of the computation process.

The end result is a waveform which correlates quite closely with that created by the test equipment. Assessment of the results provides a definitive relationship between the movement of charges along the conductor and the propagation of photons to and fro between the conductors.

Since the terminals at the far end are open-circuit, the eventual state is a constant voltage between the conductors due to charges trapped on the surfaces. But this is sustained by photons which continue to propagate to and fro between the conductors.

A method of characterising the electromagnetic coupling between a co-axial cable and the conducting structure of an electronic system is described. Frequency response tests are carried out on a rig and the data so collected is used to develop a circuit model which replicates that response. Assessment of the model provides a clear insight into the mechanisms involved in cross-coupling. This form of analysis can be integrated into the system design process.

Setup

Figure 1 shows the setup. The rig itself is a 15 mm copper pipe routed round three walls of a room. A wooden batten fixed along the top of the pipe acts as a spacer to separate the cable under test from the pipe. This setup allows different cable assemblies to be characterised. In this case it is a 50 ohm co-axial cable. One end is terminated at an interface module which allows a signal to be applied via a low impedance source and for the amplitude of that signal to be monitored by channel 1 of an oscilloscope. Both terminals at the far end are short-circuited to the copper pipe. A current transformer is used to measure the current delivered to the cable.

A transient model of a dipole antenna is developed from an earlier model which used an LCR circuit to simulate the frequency response of single conductor. A transformer at the centre provided the source voltage. The resistive component of the model was that defined by electromagnetic theory as the ‘radiation resistance’.

The new model uses a waveform generator to deliver current to the central section and shift registers to simulate the propagation of charges along the conductor. When the waveform is sinusoidal, the response is shown to be exactly the same as that of the LCR circuit.

It is reasoned that the radiation resistance provides a measure of the power used in converting the radial flow of charges in the conductor to that of photons emanating from the surface. 

Frequency Analysis

Figure 1a shows a general circuit model of a length of conductor acting as a dipole transmitter. During the first half cycle of a sinusoidal signal, the voltage source at the centre draws current from the left hand monopole and delivers it to the right hand monopole. During the second half cycle the process is reversed. When the frequency of the source corresponds to the half-wavelength of the conductor, the current reaches a maximum value, as does the radiated energy.

Ground bounce is due to supply current being switched off. All the energy stored in the supply wiring departs into the environment via the surface of the conducting structure, leaving charge on that surface, charge which manifests itself as a very high, short duration, voltage between the structure and any conductor routed along it. A test rig is used to demonstrate this, and a circuit model is used to simulate the response. 

The construction of a switching unit which can deliver a current of about 400mA and then switch that current OFF is described. This can be done at a repetition rate which allows the waveform to be monitored on a general-purpose oscilloscope. A signal generator set to give a square wave is used to control the times at which switching occurs.

The test rig consists of a twin-conductor cable routed along a copper pipe. The terminals are short-circuited at the far end. It is configured as two loops. In the culprit loop, current flows along the structure and back via one conductor. Current flowing in this loop develops a voltage between the open-circuit terminals at the near end of the victim loop.

The output of the switching unit is used to switch the supply current ON and OFF. The voltage between the terminals of the culprit loop is monitored by an ocsilloscope. This waveform shows that a high transient pulse is created at switch OFF

The test is repeated to show that the electromagnetic coupling creates a similar voltage spike in the victim loop.

A circuit model of the setup is then developed. This uses using time-step analysis to replicate the observed waveforms. It is reasoned that the voltage spike is created by current flowing out of the conducting surfaces of the scope and the signal generator, into the environment.

The significant feature of the modelling technique is that is uses the relationships of Circuit Theory to carry out the analysis. So it can be carried out by any Electrical Engineer. There is no need to invoke any of the relationships of Full Field Modelling.

Enough detailed information is provided for any circut designer to replicate the experiment.

Current transients in the conducting structure are a prolific source of interference in vehicles, aircraft, spacecraft and ships. A simple way of reducing the threat from these sources is to route a return conductor alongside each power supply conductor and connect it to the conducting structure at each end. Most of the steady-state current will flow along the structure, but the return conductor will carry the transient spikes.

An analysis was carried out on a representative assembly; a test rig. This simulates the response of a setup where a 10V step is applied to one end of a power line which delivers current to a 10 ohm load. The return conductor carries most of the return current during the first two micro-seconds. After about 20 micro-seconds the return current is shared equally between the return conductor and the ground. After 200 micro-seconds, the ground conductor carries most of the current.

Since the highest voltage spikes are due to the highest rate of change of current and since it is these spikes which affect the most sensitive circuitry, the use of dedicated return conductors will provide a significant reduction in the EMI suffered by the system.

Testing and Modelling

The test rig consists basically of a 15 mm water pipe fixed round one room of the house. A wooden batten assembled on the pipe provides a support for a cable to be routed along the length of the assembly. Various terminations can be connected at each end. Test equipment can then be used to monitor currents and voltages at one end of the line. It is possible to create a circuit model to simulate the response of any such assembly.

This rig is a fair representation of the wiring of a signal link or a of a power link assembled on a conducting structure. The copper pipe represents the structure, or ‘ground’. The cable represents any wiring harness assembled on the framework. The wooden batten provides spacing between wiring and structure. The terminations represent the interface circuitry of the equipment units installed at either end of the link.

Propagation of charge along a twin-conductor line can be simulated by a pair of shift registers and the transient response at each termination can be analysed by time-step analysis. Simulating the response of a cable routed along the structure is more complex, since the differential-mode and common-mode signals propagate at different velocities. There is also inter-mode coupling at each end.

The creation of a model which simulates such an assembly requires a high degree of confidence; confidence which can only be achieved by comparing the simulation with the results of measurements carried out on a test rig. This brings with it the requirement to simulate the test equipment as well as the assembly-under-test.

Fortunately, there existed a rig which had previously been characterised using frequency response analysis. The model derived from this exercise was transformed into one which could handle transient signals, and the test equipment re-configured to deliver and monitor square wave signals.

Photos were taken of the waveforms observed on the screen of the oscilloscope.

The task then was to create a model which simulated these waveforms. Since the setup included modules which did not form part of the equipment-under-test, these modules affected the overall response of the system to the output of the signal generator. So it was necessary to simulate the effects of the interface module at the input to the test rig, the current transformer, and to correlate the sweep time of the simulation with that of the oscilloscope.

The waveforms appearing on the screen were then compared with the response of the model. Close correlation was achieved. This established a fair degree of confidence in the technique.

It was then possible to identify that part of the simulation which represents the assembly-under-test and define this as an accurate model of that assembly. That is, as a circuit diagram with values assigned to all the components.  

A description of every aspect of the simulation is provided and a copy of the Mathcad worksheet which performs the calculations is included. Any electronics engineer can replicate the process, since it involves general-purpose test equipment and general-purpose software.  

The analysis of the drift velocity of electrons along a conductor conjures up a picture of water sluggishly flowing along a ditch in the countryside. This is misleading. A more appropriate visualisation of the flow of charges along a conductor is that of an avalanche hurtling down a mountainside.

A reprise of a lesson copied from a blackboard sixty years ago derives a figure for the drift velocity when a copper conductor is carrying its rated current. This was described as a snail’s pace. The simulation of the flow of partial currents along a transmission line provides a dramatically different scenario.

If an electron is ejected from a copper atom, that atom becomes positively charged. If an electron is attached, the charge on the atom goes negative. If photons happen to illuminate a small patch on the surface of a copper conductor, then this will initiate a chain reaction. Positive charges will depart along the wire in one direction with negative charges flowing in the other direction.

If a step voltage is applied at the near end of a twin conductor cable, then a wavefront will propagate along that cable, with positive charges flowing along one conductor and negative charges keeping pace along the other conductor.

With a short-circuited termination at the far end the chain reactions continue unabated. A negative wavefront arriving from the return conductor reappears as a positive wavefront departing along the send conductor. A positive wavefront arriving from the send conductor reappears as a negative wavefront departing along the return conductor. 

The total current at any point in a conductor is the sum of the partial currents.