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1

Sinusoidal Oscillator Circuits Reexamined

Prasad V. C.

International Journal of Electronics and Telecommunications

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2018

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Vol. 64, No. 1

77--81

EN

Singular network condition is proposed to study oscillators. It states that a circuit is a potential oscillator if and only if the rank of the network matrix of size n X n is (n -1) at the frequency of oscillations. The dual (if it exists) and adjoint circuit of an oscillator are also oscillators. Limitations of Barkhausen’s approach are pointed out. It is explained that there are many ways to generate oscillations other than Barkhausen’s positive feedback configuration. The new approach emphasizes that appropriate D C inputs / initial conditions are important.

2

Novel method to simplify Boolean functions

Prasad V. C.

Automatyka / Automatics

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2018

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Vol. 22, no. 2

29--40

EN

Most methods for determining the prime implicants of a Boolean function depend on the minterms of the function. Deviating from this philosophy, this paper presents a method that dependson maxterms (the minterms of the complement of the function) for this purpose. Normally, maxterms are used to get prime implicates and not prime implicants. It is shown that all prime implicants of a Boolean function can be obtained by expanding and simplifying any product of sums form of the function appropriately. No special form of the product of the sums is required. What is more, prime implicants can generally be generated from any form of the function by converting it into a POS using well-known techniques. The prime implicants of a product of Boolean functions can be obtained from the prime implicants of individual Boolean functions. This allows us to handle big functions by breaking them into the products of smaller functions. A simple method is presented to obtain one minimal set of prime implicants from all prime implicants without using minterms. Similar statements also hold for prime implicates. In particular, all prime implicates can be obtained from any sum of a products form.Twelve variable examples are solved to illustrate the methods.

PL

Większość metod wyznaczania implikantów prostych funkcji boolowskiej wykorzystuje mintermy funkcji. Niniejszy artykuł prezentuje odmienną metodę, która stosuje do tego celu makstermy (mintermy dopełnienia funkcji). Jest to podejście niestandardowe, gdyż zazwyczaj na podstawie makstermów uzyskuje się implicenty proste, a nie implikanty proste. W artykule pokazano, że wszystkie implikanty proste funkcji boolowskiej mogą być otrzymane przez odpowiednie rozwinięcie i uproszczenie funkcji podanej w dowolnej postaci typu iloczyn sum. Nie jest przy tym wymagana żadna szczególna postać tego iloczynu. Co więcej, implikanty proste mogą być zwykle utworzone na podstawie funkcji w dowolnej postaci, przez przekształcenie jej do postaci typu iloczyn sum z wykorzystaniem znanych metod. Implikanty proste iloczynu funkcji boolowskich można uzyskać z implikantów prostych poszczególnych funkcji. To pozwala operować na dużych funkcjach przez rozbicie ich na iloczyn mniejszych. Artykuł pokazuje prostą metodę uzyskania jednego zbioru minimalnego implikantów prostych na podstawie zbioru wszystkich implikantów prostych bez korzystania z mintermów. Podobne stwierdzenia mają zastosowanie także w przypadku implicentów prostych. W szczególności, wszystkie implicenty proste mogą być otrzymane z dowolnej formy typu suma iloczynów. Zaproponowana w artykule metoda została zilustrowana licznymi przykładami.

3

Quality of Minimal Sets of Prime Implicants of Boolean Functions

Prasad V. C.

International Journal of Electronics and Telecommunications

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2017

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Vol. 63, No. 2

165--169

EN

Two new problems are posed and solved concerning minimal sets of prime implicants of Boolean functions. It is well known that the prime implicant set of a Boolean function should be minimal and have as few literals as possible. But it is not well known that min term repetitions should also be as few as possible to reduce power consumption. Determination of minimal sets of prime implicants is a well known problem. But nothing is known on the least number of (i) prime implicants (ii) literals and (iii) min term repetitions , any minimal set of prime implicants will have. These measures are useful to assess the quality of a minimal set. They are then extended to determine least number of prime implicants / implicates required to design a static hazard free circuit. The new technique tends to give smallest set of prime implicants for various objectives.

4

Feasible star – delta and delta – star transformations for reliability networks

Prasad V. C.

Electrical Power Quality and Utilisation. Journal

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2017

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Vol. 20, no. 1

1--5

EN

Consider the problem of transforming a star (delta) into an equivalent delta (star) in a reliability network with imperfect undirected edges and perfect vertices. It is believed that such transformations are not possible in general if the probabilities of the elements of the given star / delta are rational numbers. Contrary to this, it is shown here that star – delta and delta – star transformations are possible under certain conditions. Further the probability of success of an element of an equivalent star (delta) is shown to be equal to the probability of failure of the corresponding element of the given delta (star).

5

Kirchhoff’s laws from Tellegen’s Theorem

Prasad V. C.

Electrical Power Quality and Utilisation. Journal

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2016

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Vol. 19, iss. 1

9--14

EN

It is well known that Kirchhoff’s voltage (current) law and Tellegen’s theorem (vTi = 0) imply Kirchhoff’s current (voltage) law where v and i refer to the same graph. Careful analysis shows that these statements are not applicable to practical networks unless v and i refer to different networks having the same graph. They are rewritten and proved to take care of this.