Series capacitor connection - a battery formed by a chain of capacitors. There is no branch, the output of one element is connected to the input of the next.
Physical processes with a serial connection
With a serial connection of capacitors, the charge of each is equivalent. Due to the natural principle of balance. Only extreme plates are connected to the source, others are charged by redistributing the charges between them. Using equality, we find:
q = q1 = q2 = U1 C1 = U2 C2, from which we write:
U1 / U2 = C2 / C1.
Voltages between capacitors are distributed inversely proportional to nominal capacitances. In sum, both make up the mains voltage. When discharging, the design is capable of delivering charge q no matter how many capacitors are connected in series. The capacity of the battery is found from the formula:
C = q / u = q /( U1 + U2), substituting the expressions given above, leading to a common denominator:
1 / С = 1 / С1 + 1 / С2.
Calculation of the total battery capacity of the
When the capacitors are connected in series, the opposite of the nominal capacities are added to the battery. Reducing the last expression to a common denominator, turning fractions, we get:
С = C1C2 /( C1 + C2).
The expression is used to find the battery capacity. If there are more than two capacitors, the formula becomes more complicated. To find the answer, the face values are multiplied together, the numerator of the fraction comes out. In the denominator put pairwise works of two denominations, going through combinations. In practice, it is sometimes more convenient to calculate through inverse values. The result is a split unit.
The formula is greatly simplified if the battery ratings are the same. It is required just to divide the figure by the total number of elements, obtaining the resulting value. The voltage will be distributed evenly, therefore, it is enough to divide the power supply rating equally into a total number. When the battery is powered by 12 volts, 4 tanks, 3 volts will fall on each.
We will make one simplification for the case when the ratings are equal, one capacitor is switched on to adjust the result. Then the maximum voltage of each element can be approximately found by dividing the source voltage by a reduced quantity. The result will be with a notorious margin. As for variable capacity, the requirements are much tougher. Ideally, the operating value overlaps the source voltage.
The need for a serial connection
At first glance, the idea of connecting capacitors with a battery in a sequential manner will seem to be meaningless. The first advantage is obvious: the requirements for the maximum voltage of the plates are falling. More working voltage, more expensive product. Similarly, the world is seen by a radio amateur owning a number of low-voltage capacitors, wishing to use iron as part of a high-voltage circuit.
Calculating the effective voltages by an element using the above formulas, one can easily solve the problem posed. Let us consider an example for greater clarity:
Let a battery with a voltage of 12 volts, three tanks with nominal values of 1, 2 and 4 nF, be installed. Find the voltage when the battery is connected in series.
To find the three unknowns, take the trouble to make an equal amount of the equation. It is known from the course of higher mathematics. The result will look like this:
- U1 + U2 + U3 = 12;
- U1 / U2 = 2/1 = 2, from which we write: U1 = 2U2;
- U2 / U3 = 4/2 = 2, whence it is seen: U2 = 2U
Not difficult to notice, we will substitute the last two expressions for the first, expressing 12 volts through the voltage of the third capacitor. It turns out the following:
4U3 + 2U3 + U3 = 12, from where we find, the voltage of the third capacitor is 12/7 = 1.714 volts, U2 - 3.43 volts, U1 - 6.86 volts. The sum of the numbers gives 12, each less than the voltage of the supply battery. And the greater the difference, the smaller the denomination of the neighbors. It follows from this rule: in series, low capacitors show a higher operating voltage. For definiteness, we find the nominal value of the battery, and at the same time we illustrate the formula, since the above is described purely verbally:
C = C1C2C3 /( C1C2 + C2C3 + C1C3) = 8 /( 2 + 8 + 4) = 8/14 = 571 pF.
The resulting nominal is less than each capacitor constituting a series connection. The rule shows: the maximum effect on the total capacity has a smaller one. Therefore, if it is necessary to adjust the full rating of the battery, there should be a variable capacitor. Otherwise, turning the screw will not have a big impact on the final result.
We see another pitfall: after adjustment, the voltage distribution across the capacitors will change. Calculate extreme cases so that the voltage does not exceed the operating value for the battery components.
software for researching electrical circuits In addition to the online calculators for calculating the series connection of capacitors, there are also more powerful tools. The big minus of publicly available tools is due to the reluctance of sites to check the program code, which means they contain errors. It is bad if one container fails, broken by the process of testing an improperly assembled circuit. Not the only drawback. Sometimes the scheme is much more difficult to understand the complex impossible.
In some instruments, there are high-frequency filters using a capacitor, connected in cascades. Then, in addition to the circuit through the resistor to earth, a series connection of capacitors is formed on the circuit. Usually do not apply the formula shown above. It is considered to be, each cascade of the filter exists separately, the result of the signal passing is described by the amplitude-frequency characteristic. A graph showing how strongly the spectral component of the signal will be cut off at the output.
Those who wish to make approximate calculations are advised to familiarize themselves with the Electronics Workbench software package of a personal computer. The construct is made according to English standards, take care to take into account the nuance: the designation of resistors on the electrical circuit by a broken zigzag. Denominations, the names of the elements will be spelled out in a foreign manner. Does not interfere with the use of the shell, which provides the operator with a mountain of power sources of various kinds.
And most importantly - Electronics Workbench will allow you to set test points on each, in real-time mode, look at the voltage, current, spectrum, waveform. It is supposed to supplement the project with an ammeter, voltmeter, and other similar devices.
With this software package, you simulate a situation, see how much voltage drops across a battery cell. It saves from cumbersome calculations, greatly accelerating the process of designing a circuit. Simultaneously, errors are excluded. It becomes easy and simple to add, remove capacitors with immediate result evaluation.
working example The screen shows the Electronics Workbench 5.12 desktop with the assembled capacitor wiring diagram. Each with a capacity of 1 microfarad, the same elements are taken for demonstration purposes. So that everyone can easily verify the correctness.
We first turn our attention to the source. AC voltage of 60 Hz. In the country of the developer, a different standard than the Russian one. It is recommended that you right-click the source, visit the properties, set:
- The frequency( frequency) is 50 Hz instead of 60 Hz.
- Actual voltage value( voltage) 220 volts instead of 120.
- Phase( phase - reactivity imitation) to take according to their needs.
For primers it will be useful to look through the properties of the elements of the chain. The source is free to set the voltage tolerance( percent tolerance) in percent. It is enough to add one 1 kΩ resistor, the circuit becomes a high pass filter. It is recommended not to simplify actions. Put the correct grounding mark, make sure: the circuit is completely trivial. Otherwise, the results will make you think hard for a long time.
The high-pass filter illustrated by the screen detects a rise in the amplitude-frequency characteristic in the region of 1 kHz. When finding the bandwidth should be considered: the vertical scale is logarithmic. Therefore, the cut at the level of 70% of the maximum does not correspond to seven-tenths of the height of the flat part of the peak. Avid fans will be interested in the phase response characteristic, located in the window below.
The one and the other graphs are constructed from the Analysis menu under the AC Frequency section. And also here. .. Fourier. Available to see the spectrum of the output signal. In our case, there will be nothing interesting, since we have collected a dull passive filter, the oscillation at the input is harmonic. It is much more interesting to observe the spectrum of the pulse signal.
Response Graph The Transient section shows the response to the supply of the front of the supply voltage. The graph actually shows the process of charging the battery, from where we find the time constant at the level of 0.7 maximum. Subtleties are understandable to those who want to assemble a smoothing filter amplitude detector. As can be seen from the graph, the value is 250 μs. The parameter is determined from the window as follows:
- It is considered that for three time constant of the circuit the charge of the capacitors, the discharge is approximately 95%.
- It is easy to notice that the point is in the region of 800 μs.
- Divide the value into three, you get the time constant of the battery of series-connected capacitors.
In a different way, the time constant is calculated by the product of the resistance and the total battery capacity. Using the above formulas, we calculate: C = 1 μF / 4 = 250 nF.It remains to multiply the value by 1000 ohms, you get 250 μs. The software package Electronics Workbench 5.12, with skillful use, frees up a lot of free time.
Get software electrics calculation software
There is an opinion on the Internet: the author of Electronics Workbench is a software development subsidiary of National Instruments Corporation. Not true. From the copyright window of the mentioned application, you can see: the development is done by the department of Interactive Image Technologies.
The aforementioned unit became independent in 1995.The department focused on advertising and training materials. Electronics Workbench is designed for Canadian students. Then the software product spread worldwide, for some time called Multisim.
The updated software product is sold by official dealers, the list is presented by the official site of the company National Instruments: engussia.ni.com/contact. At the time of the study, the lucky ones who got the right to buy software without leaving the city, we call the residents of Moscow, St. Petersburg. Good luck deciding to contact the official representatives, new chips have been added to Multisim:
- More than 36,000 circuit elements.
- Ability to design printed circuit boards based on the assembled circuitry.
- Advanced analysis options instead of the wretchedness shown by screenshots, a version of 20 years ago.