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Ripple (physics)
Encyclopedia
The most common meaning of ripple in electrical science
is the small unwanted residual periodic
variation of the direct current
(dc) output of a power supply which has been derived from an alternating current
(ac) source. This ripple is due to incomplete suppression of the alternating waveform
within the power supply.
As well as this time-varying phenomenon, there is a frequency domain
ripple that arises in some classes of filter
and other signal processing
networks. In this case the periodic variation is a variation in the insertion loss
of the network against increasing frequency
. The variation may not be strictly linearly periodic. In this meaning also, ripple is usually to be considered an unwanted effect, its existence being a compromise between the amount of ripple and other design parameters.
Ripple factor (γ) may be defined as the ratio of the root mean square
(rms) value of the ripple voltage
to the absolute value
of the dc component of the output voltage, usually expressed as a percentage. However, ripple voltage is also commonly expressed as the peak-to-peak value. This is largely because peak-to-peak is both easier to measure on an oscilloscope
and is simpler to calculate theoretically. Filter circuits intended for the reduction of ripple are usually called smoothing circuits.
The simplest scenario in ac to dc conversion is a rectifier
without any smoothing circuitry at all. The ripple voltage is very large in this situation; the peak-to-peak ripple voltage is equal to the peak ac voltage. A more common arrangement is to allow the rectifier to work into a large smoothing capacitor
which acts as a reservoir. After a peak in output voltage the capacitor (C) supplies the current to the load (R) and continues to do so until the capacitor voltage has fallen to the value of the now rising next half-cycle of rectified voltage. At that point the rectifiers turn on again and deliver current to the reservoir until peak voltage is again reached. If the time constant
, CR, is large in comparison to the period of the ac waveform, then a reasonably accurate approximation can be made by assuming that the capacitor voltage falls linearly. A further useful assumption can be made if the ripple is small compared to the dc voltage. In this case the phase angle
through which the rectifiers conduct will be small and it can be assumed that the capacitor is discharging all the way from one peak to the next with little loss of accuracy.
With the above assumptions the peak-to-peak ripple voltage can be calculated as:
For a full-wave rectifier:
For a half-wave rectification:
where
For the rms value of the ripple voltage, the calculation is more involved as the shape of the ripple waveform has a bearing on the result. Assuming a sawtooth wave
form is a similar assumption to the ones above and yields the result:
where
Another approach to reducing ripple is to use a series choke
. A choke has a filtering action and consequently produces a smoother waveform with less high-order harmonics. Against this, the dc output is close to the average input voltage as opposed to the higher voltage with the reservoir capacitor which is close to the peak input voltage. With suitable approximations, the ripple factor is given by:
where
More complex arrangements are possible; the filter can be an LC ladder rather than a simple choke or the filter and the reservoir capacitor can both be used to gain the benefits of both. The most commonly seen of these is a low-pass Π-filter consisting of a reservoir capacitor followed by a series choke followed by a further shunt capacitor. However, use of chokes is deprecated in contemporary designs for economic reasons. A more common solution where good ripple rejection is required is to use a reservoir capacitor to reduce the ripple to something manageable and then pass through a voltage regulator
circuit. The regulator circuit, as well as regulating the output, will incidentally filter out nearly all of the ripple as long as the minimum level of the ripple waveform does not go below the voltage being regulated to.
The majority of power supplies are now switched mode
. The filtering requirements for such power supplies are much easier to meet owing to the frequency of the ripple waveform being very high. In traditional power supply designs the ripple frequency is either equal to (half-wave), or twice (full-wave) the ac line frequency. With switched mode power supplies the ripple frequency is not related to the line frequency, but is instead related to the frequency of the chopper circuit
.
Ripple in the context of the frequency domain is referring to the periodic variation in insertion loss
with frequency of a filter or some other two-port network
. Not all filters exhibit ripple, some have monotonically
increasing insertion loss with frequency such as the Butterworth filter
. Common classes of filter which exhibit ripple are the Chebyshev filter
, inverse Chebyshev filter and the Elliptical filter. The ripple is not usually strictly linearly periodic as can be seen from the example plot. Other examples of networks exhibiting ripple are impedance matching
networks that have been designed using Chebyshev polynomials
. The ripple of these networks, unlike regular filters, will never reach 0 dB at minimum loss if designed for optimum transmission across the passband
as a whole.
The amount of ripple can be traded for other parameters in the filter design. For instance, the rate of roll-off
from the passband
to the stopband
can be increased at the expense of increasing the ripple without increasing the order of the filter (that is, the number of components has stayed the same). On the other hand, the ripple can be reduced by increasing the order of the filter while at the same time maintaining the same rate of roll-off.
Electricity
Electricity is a general term encompassing a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena, such as lightning, static electricity, and the flow of electrical current in an electrical wire...
is the small unwanted residual periodic
Periodic function
In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...
variation of the direct current
Direct current
Direct current is the unidirectional flow of electric charge. Direct current is produced by such sources as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type. Direct current may flow in a conductor such as a wire, but can also flow through...
(dc) output of a power supply which has been derived from an alternating current
Alternating current
In alternating current the movement of electric charge periodically reverses direction. In direct current , the flow of electric charge is only in one direction....
(ac) source. This ripple is due to incomplete suppression of the alternating waveform
Waveform
Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...
within the power supply.
As well as this time-varying phenomenon, there is a frequency domain
Frequency domain
In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time....
ripple that arises in some classes of filter
Filter (signal processing)
In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...
and other signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
networks. In this case the periodic variation is a variation in the insertion loss
Insertion loss
In telecommunications, insertion loss is the loss of signal power resulting from the insertion of a device in a transmission line or optical fiber and is usually expressed in decibels ....
of the network against increasing frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
. The variation may not be strictly linearly periodic. In this meaning also, ripple is usually to be considered an unwanted effect, its existence being a compromise between the amount of ripple and other design parameters.
Time-domain ripple
Root mean square
In mathematics, the root mean square , also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids...
(rms) value of the ripple voltage
Voltage
Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...
to the absolute value
Absolute value
In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign. So, for example, the absolute value of 3 is 3, and the absolute value of -3 is also 3...
of the dc component of the output voltage, usually expressed as a percentage. However, ripple voltage is also commonly expressed as the peak-to-peak value. This is largely because peak-to-peak is both easier to measure on an oscilloscope
Oscilloscope
An oscilloscope is a type of electronic test instrument that allows observation of constantly varying signal voltages, usually as a two-dimensional graph of one or more electrical potential differences using the vertical or 'Y' axis, plotted as a function of time,...
and is simpler to calculate theoretically. Filter circuits intended for the reduction of ripple are usually called smoothing circuits.
The simplest scenario in ac to dc conversion is a rectifier
Rectifier
A rectifier is an electrical device that converts alternating current , which periodically reverses direction, to direct current , which flows in only one direction. The process is known as rectification...
without any smoothing circuitry at all. The ripple voltage is very large in this situation; the peak-to-peak ripple voltage is equal to the peak ac voltage. A more common arrangement is to allow the rectifier to work into a large smoothing capacitor
Capacitor
A capacitor is a passive two-terminal electrical component used to store energy in an electric field. The forms of practical capacitors vary widely, but all contain at least two electrical conductors separated by a dielectric ; for example, one common construction consists of metal foils separated...
which acts as a reservoir. After a peak in output voltage the capacitor (C) supplies the current to the load (R) and continues to do so until the capacitor voltage has fallen to the value of the now rising next half-cycle of rectified voltage. At that point the rectifiers turn on again and deliver current to the reservoir until peak voltage is again reached. If the time constant
Time constant
In physics and engineering, the time constant, usually denoted by the Greek letter \tau , is the risetime characterizing the response to a time-varying input of a first-order, linear time-invariant system.Concretely, a first-order LTI system is a system that can be modeled by a single first order...
, CR, is large in comparison to the period of the ac waveform, then a reasonably accurate approximation can be made by assuming that the capacitor voltage falls linearly. A further useful assumption can be made if the ripple is small compared to the dc voltage. In this case the phase angle
Phase angle
In the context of vectors and phasors, the term phase angle refers to the angular component of the polar coordinate representation. The notation A\ang \!\ \theta, for a vector with magnitude A and phase angle θ, is called angle notation.In the context of periodic phenomena, such as a wave,...
through which the rectifiers conduct will be small and it can be assumed that the capacitor is discharging all the way from one peak to the next with little loss of accuracy.
For a full-wave rectifier:
For a half-wave rectification:
where
is the peak-to-peak ripple voltage
is the current in the circuit
is the frequency of the ac power
is the capacitance
For the rms value of the ripple voltage, the calculation is more involved as the shape of the ripple waveform has a bearing on the result. Assuming a sawtooth wave
Sawtooth wave
The sawtooth wave is a kind of non-sinusoidal waveform. It is named a sawtooth based on its resemblance to the teeth on the blade of a saw....
form is a similar assumption to the ones above and yields the result:
where
is the ripple factor
is the resistance of the load
Another approach to reducing ripple is to use a series choke
Choke (electronics)
A choke is a coil of insulated wire, often wound on a magnetic core, used as a passive inductor which blocks higher-frequency alternating current in an electrical circuit while passing signals of much lower frequency and direct current by having an impedance largely determined by reactance, which...
. A choke has a filtering action and consequently produces a smoother waveform with less high-order harmonics. Against this, the dc output is close to the average input voltage as opposed to the higher voltage with the reservoir capacitor which is close to the peak input voltage. With suitable approximations, the ripple factor is given by:
where
is the angular frequency 
is the inductanceInductanceIn electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
of the choke
More complex arrangements are possible; the filter can be an LC ladder rather than a simple choke or the filter and the reservoir capacitor can both be used to gain the benefits of both. The most commonly seen of these is a low-pass Π-filter consisting of a reservoir capacitor followed by a series choke followed by a further shunt capacitor. However, use of chokes is deprecated in contemporary designs for economic reasons. A more common solution where good ripple rejection is required is to use a reservoir capacitor to reduce the ripple to something manageable and then pass through a voltage regulator
Voltage regulator
A voltage regulator is an electrical regulator designed to automatically maintain a constant voltage level. A voltage regulator may be a simple "feed-forward" design or may include negative feedback control loops. It may use an electromechanical mechanism, or electronic components...
circuit. The regulator circuit, as well as regulating the output, will incidentally filter out nearly all of the ripple as long as the minimum level of the ripple waveform does not go below the voltage being regulated to.
The majority of power supplies are now switched mode
Switched-mode power supply
A switched-mode power supply is an electronic power supply that incorporates a switching regulator in order to be highly efficient in the conversion of electrical power...
. The filtering requirements for such power supplies are much easier to meet owing to the frequency of the ripple waveform being very high. In traditional power supply designs the ripple frequency is either equal to (half-wave), or twice (full-wave) the ac line frequency. With switched mode power supplies the ripple frequency is not related to the line frequency, but is instead related to the frequency of the chopper circuit
Chopper (electronics)
A chopper circuit is used to refer to numerous types of electronic switching devices and circuits. The term has become somewhat ill-defined, and as a result is much less used nowadays than it was perhaps 30 or more years ago....
.
Effects of ripple
Ripple is undesirable in many electronic applications for a variety of reasons:- The ripple frequency and its harmonics are within the audio band and will therefore be audible on equipment such as radio receivers, equipment for playing recordings and professional studio equipment.
- The ripple frequency is within television video bandwidth. Analogue TV receivers will exhibit a pattern of moving wavy lines if too much ripple is present.
- The presence of ripple can reduce the resolution of electronic test and measurement instruments. On an oscilloscope it will manifest itself as a visible pattern on screen.
- Within digital circuits, it reduces the threshold, as does any form of supply rail noise, at which logic circuits give incorrect outputs and data is corrupted.
- High-amplitude ripple currents shorten the life of electrolytic capacitors.
Frequency-domain ripple
Insertion loss
In telecommunications, insertion loss is the loss of signal power resulting from the insertion of a device in a transmission line or optical fiber and is usually expressed in decibels ....
with frequency of a filter or some other two-port network
Two-port network
A two-port network is an electrical circuit or device with two pairs of terminals connected together internally by an electrical network...
. Not all filters exhibit ripple, some have monotonically
Monotonic function
In mathematics, a monotonic function is a function that preserves the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory....
increasing insertion loss with frequency such as the Butterworth filter
Butterworth filter
The Butterworth filter is a type of signal processing filter designed to have as flat a frequency response as possible in the passband so that it is also termed a maximally flat magnitude filter...
. Common classes of filter which exhibit ripple are the Chebyshev filter
Chebyshev filter
Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple or stopband ripple than Butterworth filters...
, inverse Chebyshev filter and the Elliptical filter. The ripple is not usually strictly linearly periodic as can be seen from the example plot. Other examples of networks exhibiting ripple are impedance matching
Impedance matching
In electronics, impedance matching is the practice of designing the input impedance of an electrical load to maximize the power transfer and/or minimize reflections from the load....
networks that have been designed using Chebyshev polynomials
Chebyshev polynomials
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively. One usually distinguishes between Chebyshev polynomials of the first kind which are denoted Tn and...
. The ripple of these networks, unlike regular filters, will never reach 0 dB at minimum loss if designed for optimum transmission across the passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....
as a whole.
The amount of ripple can be traded for other parameters in the filter design. For instance, the rate of roll-off
Roll-off
Roll-off is a term commonly used to describe the steepness of a transmission function with frequency, particularly in electrical network analysis, and most especially in connection with filter circuits in the transition between a passband and a stopband...
from the passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....
to the stopband
Stopband
A stopband is a band of frequencies, between specified limits, through which a circuit, such as a filter or telephone circuit, does not allow signals to pass, or the attenuation is above the required stopband attenuation level...
can be increased at the expense of increasing the ripple without increasing the order of the filter (that is, the number of components has stayed the same). On the other hand, the ripple can be reduced by increasing the order of the filter while at the same time maintaining the same rate of roll-off.