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Updating Circuit Theory


By Ian Darney

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.


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.


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.


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  clearly shows that the wiring of the fuel system is based on the concept of the single point ground.


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.


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.


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]

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