RC circuits work as filters high-pass or low-pass filtersintegrators and differentiators. Here we explain how, and give sound files examples of RC filters in action. For an introduction to AC circuits, resistors and capacitors, see AC circuits. Low pass filter High pass filter Filter applications and demonstrations Integrator Differentiator. From the phasor diagram for this filter, we see that the output lags the input in phase.

Now a reduction in power of a factor of two means a reduction by 3 dB see What is a decibel? High pass filter The voltage across the resistor is IR.

Filter applications and demonstrations RC and other filters are very widely used in selecting signals which are voltage components one wants and rejecting noise those one doesn't want.

Conversely, a high pass filter can pass the signal into and out of a transistor amplifier stage without passing or affecting the DC bias of the transistor. They can also be used to sort high frequency from low frequency components in a purely AC signal. Capacitors are often used in 'cross over' networks for loudspeakers, to apply the high frequencies to the 'tweeter' a small, light speaker and the low frequencies to the 'woofer' a large, massive speaker. We include some sound examples here as demonstrations.

No filter. A speaker already filters the sound, because its impedance is partly inductive, due to the speaker coil. Further, its acoustic efficiency is a strong function of frequency. Nevertheless, you should notice the differences among these sound files, particularly if you switch from one to another in succession.

This sound is quieter than the previous sample. We have cut out the frequencies above 1 kHz, including those to which your ear is most sensitive. For more about the frequency response of the ear, see Hearing Curves. Losing the low frequencies makes the sound rather thin, but it doesn't reduce the loudness as much as removing the high frequencies. If you do not notice much difference with the high pass filter, it may be because you are using tiny computer speakers that do not radiate low frequencies well.

Try it with headphones or with hifi speakers. Here we have an AC source with voltage v in tinput to an RC series circuit. The output is the voltage across the capacitor. The photograph at the top of this page shows a triangle wave input to an RC integrator, and the resulting output. This time the output is the voltage across the resistor.

Wolfe unsw. There are pages on related material at LC oscillations power, RMS values and three-phase circuits Transformers Motors, generators, alternators and loudspeakers Drift velocity and Ohm's law Electricity and magnetism in Einstein's relativity Joe's scientific home page A list of educational links Music Acoustics site.

Happy birthday, theory of relativity! As of Junerelativity is years old. Our contribution is Einstein Light: relativity in brief It explains the key ideas in a short multimedia presentation, which is supported by links to broader and deeper explanations.

RC filters, integrators and differentiators From Physclips : Mechanics with animations and film. Low pass filter High pass filter Filter applications and demonstrations Integrator Differentiator A triangle wave upper trace is integrated to give a rounded, parabolic wave. From the phasor diagram for this filter, we see that the output leads the input in phase.When you use a flash camera, it takes a few seconds to charge the capacitor that powers the flash. The light flash discharges the capacitor in a tiny fraction of a second.

Why does charging take longer than discharging? This question and a number of other phenomena that involve charging and discharging capacitors are discussed in this module.

An RC circuit is one containing a resistor R and a capacitor C. The capacitor is an electrical component that stores electric charge. Figure 1 shows a simple RC circuit that employs a DC direct current voltage source. The capacitor is initially uncharged. As soon as the switch is closed, current flows to and from the initially uncharged capacitor. As charge increases on the capacitor plates, there is increasing opposition to the flow of charge by the repulsion of like charges on each plate.

This voltage opposes the battery, growing from zero to the maximum emf when fully charged. When there is no current, there is no IR drop, and so the voltage on the capacitor must then equal the emf of the voltage source. Therefore, the smaller the resistance, the faster a given capacitor will be charged. Note that the internal resistance of the voltage source is included in Ras are the resistances of the capacitor and the connecting wires.

In the flash camera scenario above, when the batteries powering the camera begin to wear out, their internal resistance rises, reducing the current and lengthening the time it takes to get ready for the next flash. Figure 1.

Current flows in the direction shown opposite of electron flow as soon as the switch is closed. Voltage on the capacitor is initially zero and rises rapidly at first, since the initial current is a maximum. The voltage approaches emf asymptotically, since the closer it gets to emf the less current flows. The equation for voltage versus time when charging a capacitor C through a resistor Rderived using calculus, is.

Note that the units of RC are seconds.

**RC Circuits Lab**

We define.An RC circuit is a circuit with both a resistor R and a capacitor C. RC circuits are freqent element in electronic devices. They also play an important role in the transmission of electrical signals in nerve cells. A capacitor can store energy and a resistor placed in series with it will control the rate at which it charges or discharges. This produces a characteristic time dependence that turns out to be exponential.

The crucial parameter that describes the time dependence is the "time constant" R C. We will confine our studies to the following circuit, in which the switch can be moved between positions a and b. Let us begin by reviewing some facts about capacitors: The charge on a capacitor cannot change instantaneously.

The current flowing into a capacitor in the steady state that is reached after a long time interval is zero. When a capacitor of capacitance C is in series with a battery of voltage V b and a resistor of resistance Rthe voltage drops must be:. We consider two instances:.

The capacitor then discharges, leaving the capacitor without charge or voltage after a long time.

### RC Snubber Circuits Importance â€“ Design & Usage

Charging the capacitor : The switch is in position b for a long time, allowing the capacitor to have no charge. Here, Q 0V 0 and I 0 refer to the charge, voltage and current of the capacitor in the instant after the switch is thrown.

When confronted with an RC problem, the best strategy is the following:. Decide what the charge across the capacitor was just before the switch was thrown. Since the charge can not change instantly, this is the charge just after the switch is thrown. Decide what the charge is long after the switch is thrown. Pick the exponential form for the charge Q t to satisfy the correct initial and final charges.

The voltages across the other elements can be found with the help of Kirchhoff's first law. The current through a capacitor must always decay and end up at zero. Every educated person should have a good feeling for exponential functions. Sketches of the charge Q t for charging and discharging capacitors could be shown here.

Discharging Charging Charge Current Voltage.Due to overheating, over voltage, over current or excessive change in voltage or current switching devices and circuit components may fail. From over current they can be protected by placing fuses at suitable locations. Heat sinks and fans can be used to take the excess heat away from switching devices and other components.

These are placed across the semiconductor devices for protection as well as to improve the performance. These are also used across the relays and switches to prevent arcing. These are placed across the various switching devices like transistors, thyristors, etc.

Switching from ON to OFF state results the impedance of the device suddenly changes to the high value. But this allows a small current to flow through the switch. This induces a large voltage across the device.

If this current reduced at faster rate more is the induced voltage across the device and also if the switch is not capable of withstanding this voltage the switch becomes burn out. So auxiliary path is needed to prevent this high induced voltage.

Similarly when the transition is from OFF to ON state, due to uneven distribution of the current through the area of the switch overheating will takes place and eventually it will be burned. Here also snubber is necessary to reduce the current at starting by making an alternate path. There are many kinds of snubbers like RC, diode and solid state snubbers but the most commonly used one is RC snubber circuit. This is applicable for both the rate of rise control and damping. This circuit is a capacitor and series resistor connected across a switch.

For designing the Snubber circuits. The amount of energy is to dissipate in the snubber resistance is equal to the amount of energy is stored in the capacitors. An RC Snubber placed across the switch can be used to reduce the peak voltage at turn-off and to lamp the ring. An RC snubber circuit can be polarized or non-polarized. If you assume the source has negligible impedance, the worst case peak current in the snubber circuit is. For an appropriate forward-polarized RC snubber circuit a thyristor or a transistor is connected with an anti-parallel diode.

These are used as overvoltage snubbers to clamp the voltage. R1 will limit the discharge current of the capacitor. An un-polarized snubber circuit is used when a pair of switching devices is used in anti-parallel.

For determining the resistor and capacitor values a simple design technique can be used. For this an optimum design is needed. Hence a complex procedure will be used. These can be used to protect and thyristors. An example is turn-on and turn-off current spikes in a typical RCD snubber capacitor.

The pulse will have high peak and RMS amplitudes. The snubber capacitor has to meet two requirements.The first step is to identify the starting and final values for whatever quantity the capacitor or inductor opposes the change in; that is, whatever quantity the reactive component is trying to hold constant.

For capacitorsthis quantity is voltage ; for inductorsthis quantity is current. The final value for this quantity is whatever that quantity will be after an infinite amount of time.

The next step is to calculate the time constant of the circuit: the amount of time it takes for voltage or current values to change approximately 63 percent from their starting values to their final values in a transient situation. In a series RC circuitthe time constant is equal to the total resistance in ohms multiplied by the total capacitance in farads. The rise and fall of circuit values such as voltage and current in response to a transient are, as was mentioned before, asymptotic.

Being so, the values begin to rapidly change soon after the transient and settle down over time. If plotted on a graph, the approach to the final values of voltage and current form exponential curves. As was stated before, one time constant is the amount of time it takes for any of these values to change about 63 percent from their starting values to their ultimate final values. For every time constant, these values move approximately 63 percent closer to their eventual goal.

The mathematical formula for determining the precise percentage is quite simple:. It is derived from calculus techniques, after mathematically analyzing the asymptotic approach of the circuit values.

The more time that passes since the transient application of voltage from the battery, the larger the value of the denominator in the fraction, which makes for a smaller value for the whole fraction, which makes for a grand total 1 minus the fraction approaching 1, or percent. We can make a more universal formula out of this one for the determination of voltage and current values in transient circuits, by multiplying this quantity by the difference between the final and starting circuit values:.

The final value, of course, will be the battery voltage 15 volts. Our universal formula for capacitor voltage in this circuit looks like this:. So, after 7. Since we started at a capacitor voltage of 0 volts, this increase of The same formula will work for determining the current in that circuit, too. We also know that the final current will be zero, since the capacitor will eventually behave as an open-circuit, meaning that eventually, no electrons will flow in the circuit.

Now that we know both the starting and final current values, we can use our universal formula to determine the current after 7. Note that the figure obtained for change is negative, not positive! This tells us that the current has decreased rather than increased with the passage of time. Since we started at a current of 1. Either way, we should obtain the same answer:.

The universal time constant formula also works well for analyzing inductive circuits. If we start with the switch in the open position, the current will be equal to zero, so zero is our starting current value. If we desired to determine the value of current at 3. Given the fact that our starting current was zero, this leaves us at a circuit current of Subtracted from our battery voltage of 15 volts, this leaves 0. View our collection of Power Calculators in our Tools section. In Partnership with Avnet Silica.

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## Microelectronic Circuits Sedra Smith 7th Edition [Chegg Solutions].pdf

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But otherwise, the idea that all-flash arrays are more expensive than high-performance hard drive based systems is a myth, according to Herzog. On cost per GB, he thinks they are on par. Once you factor in the extensive abilities for data reduction, they can be less expensive per GB. This will spur further development in the software and analytics fields. Boudreau pointed to machine learning as a key enabler. Please enable Javascript in your browser, before you post the comment.

Now Javascript is disabled. You have characters left. The ERP is the premium you get from holding stocks, expressed as a percentage over some supposed risk-free measure such as the 10-year gilt rate. And there's nothing wrong with that. It's true that most often investors are rewarded long term for taking extra volatility risk. Since 1926, the average annualised ERP has been 4.

And theoretically, investors should be rewarded for suffering through stock market swings. If you weren't likely to get higher reward for higher risk, why would anyone want the higher risk.

The problem is that some academics try to model future ERPs - predicting future stock returns. I've never seen any ERP model stand up to historical back-testing. Yet every year, we get a new wave of them. When I say future, I mean most ERPs attempt forecasting far into the future - usually seven to 10 years (10 is most common). Yet stock returns in the near term - over the next 12 to 24 months - are driven mostly by shifts in demand, and even those are devilishly difficult to forecast.

Further out, supply pressures swamp all, so there is absolutely no way to predict stock market direction seven or 10 years out unless you can somehow predict future stock supply shifts. But not a single ERP model I've ever seen has addressed the issue of predicting long-term supply flows. And if you can't address future supply, your model is worthless because with securities, in the long term supply is all that matters.

None of these ERPs stands up to historical back-testing, or if they do it's merely accidentalInstead, most ERP models make forward-looking assumptions based on cobbled-together current or past conditions.

But right away you know past performance is never, by itself, indicative of future results. An example of an ERP model might look like this: take the current dividend yield, the average earnings per share over the last 10 years, plus the current inflation rate, and subtract the bond yield. Add or subtract a few components.