Cutoff frequency - Wikipedia
frequency components and / or their phase relationships. Note that monotonic, with a low-pass or high-pass rolloff rate of 20dB/decade (6dB/Octave) per pole. Notice that the only difference between the curves for jco and for l/jco is a For the factor (jco)±m the Lm curve has a slope of twi/ dB/octave or ±20m dB/decade of co > 1/ T this function is a straight line with a negative slope of 6dB /octave. How to convert decibel/decade to decibel/octave? pole filter) of 6dB/octave and 20dB/decade and they are related by the value I gave above.
A digital FIR filter design alternative to the window technique that allows designers to achieve a desired frequency response with the fewest number of coefficients. The ratio of output signal amplitude to input signal amplitude. The difference of output signal amplitude to input signal amplitude expressed in decibels. Geometric Center Frequency Fo: The instantaneous rate of change of phase with respect to frequency of a filter, usually shown in a phase versus frequency plot.
A signal whose frequency of interest is an integer multiple of the fundamental frequency, i. Infinite Impulse Response Digital Filter consists of the equivalent of both poles and zeros, generally implemented with a floating point DSP processor and capable of mathematically emulating most analog filters. Algorithms that utilize previously calculated values in future calculations. A collection of filters specifically designed with gain and phase matched responses for multi-channel systems where channel-to-channel differences must be minimized.
Constantly increasing attenuation with frequency. A repetitive delay-and-add format utilized in fixed-point math. The finite number of "n" delay taps on a delay line and "n" computation coefficients needed to compute a digital filter algorithm. The ratio between a fixed reference and a variable value, both having the same fundamental physical units.
Unwanted signals that distort or affect the signals of interest, and one of the reasons filters are used. Noise may come from external sources Radiated noise such as EMI be generated by system components Amplifiers, resistors or clocks or just may be an undesirable part of the signal itself. A doubling or halving, usually applied to frequency.
This term is usually associated with Chebychev and Cauer elliptic filters. Range of frequencies throughout which a filter passes signals with no change. The time interval, which sine waves or other periodic waveforms repeats.
The angular measure of the difference in that starting point of two sine waves or periodic signals. Measured in degrees or radians. These filters are designed to achieve a desired phase response, i.
Preserve linear phase with frequency throughout the filter amplitude pass-band in order to preserve a transient waveform. Is the phase difference in degrees between the filter input and output signals. Phase will typically shift with changes in frequency. Values of complex frequency, which make the transfer function infinite. Factors in the denominator of the transfer function polynomial.
20db/decade = 6db/octave
A variation in amplitude within the pass-band of amplitude filters. Mathematically related to the filter transfer function, settling time See Delay represents the time required for a filter transfer function to stabilize following introduction of a signal.
General guide-line, the more the filter approaches a brick-wall approximation, the longer it will take to settle. The response of a filter to a sudden change in voltage amplitude at the filter See Amplitude Filters input can result in overshoot ringing. Yet another might be to compensate for specific characteristics of your speaker system. The purpose of analyzing these circuits is to gain insight into the frequency response of an existing or proposed amplifier. This is often useful before attempting to alter the response, as it provides a way of predicting what effect a proposed change might have.
This tutorial will work through some background material describing what alters frequency response, and how to apply this knowledge to several circuit examples. These are the "frequency domain" response manipulating concepts. A pole causes the frequency response to tip "clockwise" at 6 dB per octave 20 dB per decade.
A zero causes the frequency response to tip "counterclockwise" at 6 dB per octave. At the "corner" frequency, the response is altered by 3 dB and by 45 degrees.
A clockwise bend is 45 degrees lag, a counterclockwise bend is 45 degrees lead. Poles can be "bought" for your intended circuit fairly cheaply, while zeros at anything other than DC usually "cost".
Practically, what this means is it's easy to "roll off" response by incorporating a capacitor, but difficult to achieve a "boosted response": This will be clarified later. An example of a pole is an RC network: It also has a zero at "infinite frequency". Its frequency response looks like this: Note the difference between the idealized pole response greenand the frequency response actually achieved red.
The real response is 3dB down at the calculated pole's frequency. There are additional observations to be made. At exactly the "corner", the actual response differs from the idealized response by 3dB. At exactly one octave away at Hz and at 2kHz in the examplethe error from "ideal" is exactly 1dB. At 2 octaves away at Hz and 4kHz in the examplethe error from "ideal" is 0. At 3 octaves away at Hz and 8kHz in the examplethe error is 0. We will use this later to estimate the "synthesis" of a complex response.
Note that in this picture, as above, the idealized pole is shown in green and the actual response is shown in red. If the response was flat, a pole will cause the response to fall at 6dB per octave above the pole frequency. If the response was rising at 6dB per octave, a pole will cause the response to flatten above the pole frequency.
If the response was falling at 6dB per octave, a pole will cause the response to fall at 12dB per octave above the pole frequency. If the response was flat, a zero will cause the response to rise at 6 dB per octave above the zero frequency. If the response was rising at 6dB per octave, a zero will cause the response to rise at 12 dB per octave above the zero frequency.
If the response was falling at 6dB per octave, a zero will cause the response to flatten above the zero frequency. A pole is "free". That is, it is always possible to get the response to tilt downward or flatten if it was rising with only passive components.
That is, it is essentially impossible to get a free zero. In order to get response to tilt up, you must lower the entire level by the required "tilt up". Then you can buy a zero to tilt the response up, and the "automatic" pole will flatten the response when you have "used up" the originally dropped level. I know this is confusing: In this case, we must first accept 14 dB of overall loss below the zero. When we get to "0dB loss" at 5kHz in this example there will be a pole to flatten the response again.
Poles CAN occur at zero frequency. One example is the phase comparator of a phase locked loop. A pole at DC is called a true integrator. A zero may also be called a differentiator.
However, since you can't buy a zero without buying a pole, there are no true differentiators. Another way of looking at this is a true differentiato would require infinite gain at infinite frequency, which also equates to infinite energy! Those of you who have taken calculus can appreciate this. Series R, C to ground low pass: Series C, R to ground high pass: Series R, L to ground high pass: Series L, R to ground low pass: Impedance increases away from resonance.
Impedance decreases away from resonance. Consider an R-C coupling mechanism from plate of one stage to grid of the next stage. What is the frequency response?