Electronics Engineering

Reactance of capacitor is inversely proportional to frequency. I should not need to write the exact equation here, its in your textbook. All you need is that its inversely proportional to frequency for proof.

We will now assume an ideal capacitor to keep the analysis simple.

• at DC the frequency is zero, the inverse of this is infinite reactance: open circuit
• at low frequency AC frequency is low, the inverse of this is high reactance
• at midrange frequency AC frequency is midrange, the inverse of this is midrange reactance
• at high frequency AC frequency is high, the inverse of this is low reactance
• at infinite frequency AC frequency is infinite, the inverse of this is zero reactance: short circuit

This disproves your original statement as written, except for the special cases of DC and infinite frequency AC (which does not occur), for ideal capacitors.

As all real capacitors are nonideal, they have leakage resistance. This means that even for the special case of DC the capacitor is not a true open circuit, just a very high resistance resistor. Which also disproves it for the remaining case of DC in real capacitors.

A, B and C are inputs, Q is output.

A B C Q

0 0 0 1

0 0 1 0

0 1 0 0

0 1 1 1

1 0 0 0

1 0 1 1

1 1 0 1

1 1 1 0

*update*

Although the Logism software shows the 3 input XNOR gate output 1 when all 3 are 1, perhaps there is a mistake, and 3 input of 1,1,1 in an XNOR gate

outputs 0. There is a good reason why. In an XOR gate, an even amount of 1 or 0 input will output a 0, and an odd input of 1 (ie: 1, 1, 1) will output a 1. The truth table

for an XOR gate with 1, 1, 1 input is an output of 1. An XNOR gate will output the opposite of an XOR gate, thus XNOR input of

1, 1, 1 should output 0.

''http://mems.caltech.edu/courses/EE40%20Web%20Files/Supplements/02_Hall_Effect_Derivation.pdf''

All the derivation is precisely explained.

You need to equate Newton second law to Lorentz equation, assuming the magnetic field is normal to current flow. You need do this separately for electrons and for holes. Both velocity and electric field have two components, transversal (y) and longitudinal (x) and the magnetic field is in z. It is more comfortable separate the vectorial equations into two equations, one for each component. So, you have four equations:
1) For time derivative of x-velocity of electrons
2) For time derivative of x-velocity of holes
3) For time derivative of y-velocity of electrons
4) For time derivative of y-velocity of holes


The set is complicate, but it is easier if you do the following approximation:
If magnetic field is small, you can assume that the second term in equations 1) and 2) is negligible. Yo cannot do the same with equations 3) and 4) because, since mobility of electrons and holes are not much different, this would give you as a result that transversal field does not exist, and you will not get anything.

You must bear in mind that velocities in your equations are individual velocities and you need average velocities. If you use the single model of a carrier starting from zero velocity and accelerating at a constant rate and suddenly stopped at a time tau, you can obtain the average velocities for the four equations multiplying the right side of each times tau/2. You can make sense of all this by plotting changing velocity as a saw tooth signal.

In agreement with mobility definition (charge times half-tau over effective mass) you can see that equations 1) and 2) are no more that the classic lineal relation between average velocity and electric field, with the mobility as a constant. Equations 3) and 4) have both a similar first term but the second term, including the magnetic field is more weird.

Now, you have average x-velocity for electrons, average x-velocity for holes, average y-velocity for electrons and average y-velocity for holes. If you multiply each velocity by charge and concentration you will get x-current density for electrons, x-current density for holes, y-current density for electrons and y-current density for holes. When this is done, you can add contributions of both types of carriers and obtain x-current density and y-current density.

What you will use for calculating the Hall´s coefficient is transversal current density which must be zero. Replace this zero in the formula for y-current density and you will obtain two terms equated to zero or rearranging, an equality between two terms. One of the terms is already in the shape we want, but the other still include longitudinal velocities for electrons and holes. You have expressions for them and must replace in the expression for y-current density. Now, you must identify expressions that can be replaced by electron and hole mobilities.

Now, you only have carrier concentrations, carrier mobilities, longitudinal and transversal fields and magnetic field magnitude. Solve for transversal electric field. For obtaining Hall´s coefficient you need to multiply both numerator and denominator for conductivity. Keep conductivity in the denominator in terms of concentrations and mobilities. This is not important for the numerator because you will must note that conductivity times longitudinal electric field is longitudinal density current. Now you have transversal electric field as a linear function of the product of current density (longitudinal, the only non-zero current density) times the magnetic field magnitude. The proportionality constant is Hall´s coefficient.

It is not easy!

Lydia Alvarez, Mexicali B.C. Mexico
lydia@iing.mxl.uabc.mx

For an electrical device, such as a lamp for example, to operate at its rated power, it must be supplied with its rated voltage. If several such devices are to be connected to the same circuit, the only way to achieve this requirement is to connect the devices in parallel (because the same voltage appears across each branch of a parallel circuit). Furthermore, with parallel connections, if one device should fail (or simply get switched off), all the other devices will continue to operate normally. These are the two reasons why most practical circuits are parallel circuits.

Series circuits are less common but can be used for some lighting circuits (e.g. Christmas decorations) in which case the supply voltage is distributed equally across each of the lamps, which then have appropriately-rated voltages. For example, you may have twenty-four, 10-V lamps, connected in series across a 240-V supply.

PNP

• Operates on minority charge carriers (holes).
• Slower than NPN because holes are less mobile than electrons.
• Slightly easier to manufacture than NPN.
• More sensitive to high temperature due to thermal hole generation.
• etc.

NPN

• Operates on minority charge carriers (electrons).
• Faster than PNP because electrons are more mobile than holes.
• Slightly harder to manufacture than PNP.
• Less sensitive to high temperature.
• etc.