Cutoff Frequency: What is it? Formula And How To Find it
Cutoff Frequency: What is it? Formula And How To Find it
Contents
- Cutoff Frequency Defined: Cutoff frequency is defined as the point in a frequency response at which the signal begins to be attenuated rather than fully passing through.
- Formula and Calculation: The cutoff frequency is calculated by taking 1 divided by the product of two times pi, the resistance, and the capacitance. This shows how the frequency at which the output signal power is halved is directly influenced by the resistance and capacitance values.
- Understanding Bandwidth: Bandwidth is the difference between the upper and lower cutoff frequencies, crucial for applications like audio processing where a flat response is desired.
- Decibel Significance: Gain in circuits is expressed in decibels, a logarithmic unit that matches the human ear’s response, important for understanding signal amplification and attenuation.
- Method of Finding: Cutoff frequency can be calculated using transfer functions or visualized on Bode plots, aiding in the design and analysis of electrical filters.
What is Cutoff Frequency?
Cutoff frequency (also known as corner frequency, or break frequency) is defined as a boundary in a system’s frequency response at which energy flowing through the system begins to be attenuated (reflected or reduced) rather than passing through.
The cutoff frequency or corner frequency in electronics is the frequency either above or below which the power output of a circuit, such as a line, amplifier, or electronic filter (e.g. a high pass filter) has fallen to a given proportion of the power in the passband.
Most frequently this proportion is one-half the passband power, also referred to as the 3 dB point since a fall of 3 dB corresponds approximately to half power. As a voltage ratio, this is a fall to approximately 0.707.
For any filtering circuits such as RC circuits, the cutoff frequency is a very important characteristic. At this point, the amount of attenuation due to the filter starts to increase swiftly.
To indicate how long the amplifier gain can remain constant in frequency, we need to define a range of frequencies. Along with that range, the gain should not deviate more than 70.7% of the maximum gain that has been defined as a reference at mid-frequency. In the below-shown curve, f1 and f2 indicate lower cut-off and upper cut-off frequencies.
What is Bandwidth?
In signal processing, bandwidth is defined as the difference between the upper cutoff frequency and low cutoff frequency. The frequency f2 lies along with a high-frequency range and f1 in the low-frequency range. We can also name these two frequencies as Half–Power frequencies since voltage gain drops to 70.7 % of the maximum value.
This represents the power level of one–half of the power at the reference frequency in the mid-range frequency. Since the change is not noticeable, the audio amplifier has a flat response from f1 to f2.
Cutoff Frequency Formula
The formula for cutoff frequency (corner frequency) is
  
where R and C are the values of Resistance and Capacitance. For a simple RC low pass filter, cut-off (3dB point) is defined as when the resistance is the same magnitude as the capacitive reactance
Decibel Unit
Gain is often measured in decibels, reflecting the logarithmic way our ears perceive sound. This unit measures the power or voltage ratio logarithmically.
Generally, the voltage output or voltage gain of an amplifier is expressed in decibels (dB) which is given by Voltage gain in dB is 
.
The power gain of the amplifier is expressed in decibels (dB) which is given by power gain in dB is 
When Av is greater than one, it is said that dB gain is positive. It represents the amplification. When Av is less than one, dB is negative. It represents attenuation.
In some cases, amplifier gain is set to a 0 dB reference. This serves as a baseline to compare other gain levels.
Amplifiers show a maximum gain in the mid-frequency range and reduced gain in the low-frequency range. Maximum gain is called the mid-frequency range with a value of 0 dB. When the gain value is below the mid-frequency range, it is expressed as a negative dB value.
