# Resistor theory and technology 2001 pdf

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Published: 10.06.2021  The parallel operator represents the reciprocal value of a sum of reciprocal values sometimes also referred to as "reciprocal formula" and is defined by:    . The operator gives half of the harmonic mean of two numbers a and b. The concept has been extended from a scalar operation to matrices      and further generalized. For addition , the parallel operator follows the commutative law :. Multiplication is distributive over this operation.

## Negative resistance

In electronics , negative resistance NR is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it. This is in contrast to an ordinary resistor in which an increase of applied voltage causes a proportional increase in current due to Ohm's law , resulting in a positive resistance. Negative resistance is an uncommon property which occurs in a few nonlinear electronic components.

In general, a negative differential resistance is a two-terminal component which can amplify ,   converting DC power applied to its terminals to AC output power to amplify an AC signal applied to the same terminals. Most microwave energy is produced with negative differential resistance devices.

In addition, circuits containing amplifying devices such as transistors and op amps with positive feedback can have negative differential resistance. These are used in oscillators and active filters. Because they are nonlinear, negative resistance devices have a more complicated behavior than the positive "ohmic" resistances usually encountered in electric circuits. Unlike most positive resistances, negative resistance varies depending on the voltage or current applied to the device, and negative resistance devices can only have negative resistance over a limited portion of their voltage or current range.

Negative resistance occurs in a few nonlinear nonohmic devices. Negative resistance, like positive resistance, is measured in ohms. Conductance is the reciprocal of resistance. It can be seen that the conductance has the same sign as its corresponding resistance: a negative resistance will have a negative conductance [note 1] while a positive resistance will have a positive conductance.

One way in which the different types of resistance can be distinguished is in the directions of current and electric power between a circuit and an electronic component. The illustrations below, with a rectangle representing the component attached to a circuit, summarize how the different types work:. Occasionally ordinary power sources are referred to as "negative resistances"     fig. Electronic components with negative differential resistance include these devices:.

Electric discharges through gases also exhibit negative differential resistance,   including these devices. In addition, active circuits with negative differential resistance can also be built with amplifying devices like transistors and op amps , using feedback. Therefore, some authors    state that static resistance can never be negative. This is opposite to the direction of current in a passive device defined by the passive sign convention so the current and voltage have opposite signs, and their ratio is negative.

This can also be proved from Joule's law   . The absolute resistance of power sources is negative,   but this is not to be regarded as "resistance" in the same sense as positive resistances. The negative static resistance of a power source is a rather abstract and not very useful quantity, because it varies with the load. Due to conservation of energy it is always simply equal to the negative of the static resistance of the attached circuit right.

Work must be done on the charges by some source of energy in the device, to make them move toward the positive terminal against the electric field, so conservation of energy requires that negative static resistances have a source of power.

A circuit cannot have negative static resistance be active over an infinite voltage or current range, because it would have to be able to produce infinite power. Therefore, the ends of the I—V curve will eventually turn and enter the 1st and 3rd quadrants. For example, applying a voltage to a generator or battery graph, above greater than its open-circuit voltage  will reverse the direction of current flow, making its static resistance positive so it consumes power.

Similarly, applying a voltage to the negative impedance converter below greater than its power supply voltage V s will cause the amplifier to saturate, also making its resistance positive. In a device or circuit with negative differential resistance NDR , in some part of the I—V curve the current decreases as the voltage increases: . The I—V curve is nonmonotonic having peaks and troughs with regions of negative slope representing negative differential resistance.

Passive negative differential resistances have positive static resistance;    they consume net power. Therefore, the I—V curve is confined to the 1st and 3rd quadrants of the graph,  and passes through the origin. This requirement means excluding some asymptotic cases that the region s of negative resistance must be limited,   and surrounded by regions of positive resistance, and cannot include the origin.

Negative differential resistances can be classified into two types:  . Most devices have a single negative resistance region. However devices with multiple separate negative resistance regions can also be fabricated. An intrinsic parameter used to compare different devices is the peak-to-valley current ratio PVR ,  the ratio of the current at the top of the negative resistance region to the current at the bottom see graphs, above :.

The larger this is, the larger the potential AC output for a given DC bias current, and therefore the greater the efficiency. A negative differential resistance device can amplify an AC signal applied to it   if the signal is biased with a DC voltage or current to lie within the negative resistance region of its I—V curve.

The tunnel diode circuit see diagram is an example. In a normal voltage divider, the resistance of each branch is less than the resistance of the whole, so the output voltage is less than the input. The diagrams illustrate how a biased negative differential resistance device can increase the power of a signal applied to it, amplifying it, although it only has two terminals.

With the proper external circuit, the device can increase the AC signal power delivered to a load, serving as an amplifier ,  or excite oscillations in a resonant circuit to make an oscillator. Unlike in a two port amplifying device such as a transistor or op amp, the amplified signal leaves the device through the same two terminals port as the input signal enters.

In a passive device, the AC power produced comes from the input DC bias current,  the device absorbs DC power, some of which is converted to AC power by the nonlinearity of the device, amplifying the applied signal. Therefore, the output power is limited by the bias power . The negative differential resistance region cannot include the origin, because it would then be able to amplify a signal with no applied DC bias current, producing AC power with no power input.

The "reflected" output signal has larger amplitude than the incident; the device has "reflection gain". Because it is nonlinear, a circuit with negative differential resistance can have multiple equilibrium points possible DC operating points , which lie on the I—V curve. However, because of the different shapes of the curves, the condition for stability is different for VCNR and CCNR types of negative resistance:  .

For general negative resistance circuits with reactance , the stability must be determined by standard tests like the Nyquist stability criterion. For stability []. In addition to the passive devices with intrinsic negative differential resistance above, circuits with amplifying devices like transistors or op amps can have negative resistance at their ports.

The circuit acts like a "negative linear resistor"    [] over a limited range,  with I—V curve having a straight line segment through the origin with negative slope see graphs. In circuit theory these are called "active resistors". Considered as one-port devices, these circuits function similarly to the passive negative differential resistance components above, and like them can be used to make one-port amplifiers and oscillators   with the advantages that:.

The I—V curve can have voltage-controlled "N" type or current-controlled "S" type negative resistance, depending on whether the feedback loop is connected in "shunt" or "series". Negative reactances below can also be created, so feedback circuits can be used to create "active" linear circuit elements, resistors, capacitors, and inductors, with negative values.

This is how feedback oscillators such as Hartley or Colpitts oscillators work. These have high losses and low Q, so to create high Q tuned circuits their Q is increased by applying negative resistance.

Circuits which exhibit chaotic behavior can be considered quasi-periodic or nonperiodic oscillators, and like all oscillators require a negative resistance in the circuit to provide power.

A common example of an "active resistance" circuit is the negative impedance converter NIC   [] [] shown in the diagram.

So the input impedance to the circuit is . An NIC can cancel undesired positive resistance in another circuit, [] for example they were originally developed to cancel resistance in telephone cables, serving as repeaters. Applying a positive current to a negative capacitance will cause it to discharge ; its voltage will decrease. A circuit having negative capacitance or inductance can be used to cancel unwanted positive capacitance or inductance in another circuit.

There is also another way of looking at them. Negative capacitances and inductances are "non-Foster" circuits which violate Foster's reactance theorem.

Negative differential resistance devices are widely used to make electronic oscillators. Negative resistance oscillators are mainly used at high frequencies in the microwave range or above, since feedback oscillators function poorly at these frequencies. They are a widely used source of microwave energy, and virtually the only solid-state source of millimeter wave [] and terahertz energy [] Negative resistance microwave vacuum tubes such as magnetrons produce higher power outputs, [] in such applications as radar transmitters and microwave ovens.

Lower frequency relaxation oscillators can be made with UJTs and gas-discharge lamps such as neon lamps. The negative resistance oscillator model is not limited to one-port devices like diodes but can also be applied to feedback oscillator circuits with two port devices such as transistors and tubes.

At microwave frequencies, transistors with certain loads applied to one port can become unstable due to internal feedback and show negative resistance at the other port. The common Gunn diode oscillator circuit diagrams  illustrates how negative resistance oscillators work. Solving this equation gives a solution of the form . Practical oscillators are designed in region 3 above, with net negative resistance, to get oscillations started.

However, the oscillations cannot grow forever; the nonlinearity of the diode eventually limits the amplitude. Negative resistance oscillator circuits can be divided into two types, which are used with the two types of negative differential resistance — voltage controlled VCNR , and current controlled CCNR  []. Most oscillators are more complicated than the Gunn diode example, since both the active device and the load may have reactance X as well as resistance R.

Modern negative resistance oscillators are designed by a frequency domain technique due to K. For steady-state oscillation the equal sign applies.

During startup the inequality applies, because the circuit must have excess negative resistance for oscillations to start. Alternately, the condition for oscillation can be expressed using the reflection coefficient.

During operation the waves are reflected back and forth in a round trip so the circuit will oscillate only if  [] []. As above, the equality gives the condition for steady oscillation, while the inequality is required during startup to provide excess negative resistance. The above conditions are analogous to the Barkhausen criterion for feedback oscillators; they are necessary but not sufficient, [] so there are some circuits that satisfy the equations but do not oscillate.

Kurokawa also derived more complicated sufficient conditions, [] which are often used instead. Negative differential resistance devices such as Gunn and IMPATT diodes are also used to make amplifiers , particularly at microwave frequencies, but not as commonly as oscillators. One widely used circuit is the reflection amplifier in which the separation is accomplished by a circulator. In the reflection amplifier diagram the input signal is applied to port 1, a biased VCNR negative resistance diode N is attached through a filter F to port 2, and the output circuit is attached to port 3.

The input signal is passed from port 1 to the diode at port 2, but the outgoing "reflected" amplified signal from the diode is routed to port 3, so there is little coupling from output to input. The purpose of the filter F is to present the correct impedance to the diode to set the gain. At radio frequencies NR diodes are not pure resistive loads and have reactance, so a second purpose of the filter is to cancel the diode reactance with a conjugate reactance to prevent standing waves.

The filter has only reactive components and so does not absorb any power itself, so power is passed between the diode and the ports without loss. The input signal power to the diode is.

In practice the gain is limited by the backward "leakage" coupling between circulator ports. ## Negative resistance

Chitralekha Mahanta. However you can help us serve more readers by making a small contribution. A basic understanding of microcontrollers and electronics is also expected. Referring to the basic operational amplifier depicted above, we note that resistors and form a voltage divider. These have led to the introduction of new applications that were not possible with discrete devices.

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## Electrical Circuit Theory and Technology, Fourth Edition

A force-sensing resistor is a material whose resistance changes when a force , pressure or mechanical stress is applied. They are also known as "force-sensitive resistor" and are sometimes referred to by the initialism "FSR". The technology of force-sensing resistors was invented and patented in by Franklin Eventoff. In Eventoff founded a new company, Sensitronics,  that he currently runs.

### Electronic Circuits Pdf

In electronics , negative resistance NR is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it. This is in contrast to an ordinary resistor in which an increase of applied voltage causes a proportional increase in current due to Ohm's law , resulting in a positive resistance. Negative resistance is an uncommon property which occurs in a few nonlinear electronic components. In general, a negative differential resistance is a two-terminal component which can amplify ,   converting DC power applied to its terminals to AC output power to amplify an AC signal applied to the same terminals. Most microwave energy is produced with negative differential resistance devices.

In this session, we start a new unit on circuits. We will explore different motivations for studying circuits, the conventional representations associated with the study of circuits, and Kirchhoff's voltage and current laws. The overview handout provides a more detailed introduction, including the big ideas of the session, key vocabulary, what you should understand theory and be able to do practice after completing this session, and additional resources. PDF | One of the most used electrical components in measuring systems is apparently the simple resistor. It is used 2 Basic Theory of Resistance mount technology. Schlabbach, J. () Voltage Quality in Electrical Power Sys-.