Visualizing Series Bandpass Filters: A Graphical Approach

In summary, the conversation discusses the theoretical graph of a complex impedance equation for the RLC series and the measurement of the real ratio of two amplitudes. It is mentioned that the measured ratio can deviate due to the influence of the measurement equipment and it is important to check the values of components and equipment. The use of complex number arithmetic and understanding of impedance representation is necessary for understanding this concept. Additionally, the conversation mentions the importance of knowledge in simple circuit analysis, particularly voltage dividers, and suggests resources for further learning.
  • #1
so_gr_lo
69
10
Homework Statement
I am plotting Vout/Vin against frequency for a RLC series bandpass filter, where Vout is across the resistor. The resulting graph has max Vout/Vin of about 1.5, the max is supposed to be 1 in a bandpass filter. The Vout/Vin values are experimental, could a max Vout/Vin of 1.5 occur in an experiment? And what could be the reason for this?
Relevant Equations
Vin/Vout = R / (R+wL -1/wc) , where w = omega
this is the circuit
1648543482474.png


this is the theoretical graph

1648543876109.png
 
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  • #2
Hi,

Your relevant equation is an equation with complex quantities on both sides.
(I think you switched in and out subscripts ?)

What you measure is most likely the real ratio of two amplitudes. As plotted in the theoretical graph.
For the complex impedance of the RLC series we have $$Z^2 = R^2 + \left (\omega L - {1\over \omega C}\right )^2 $$ with a minimum ##Z=R## (and ##V_{out}/V_{in}=1## ).

A measured ratio can deviate if the measurement equipment influences the circuit. So you have to check values of components and equipment.

##\ ##
 
  • #3
So what equation could you use to plot theoretical values of Vout / Vin ?
 
  • #4
so_gr_lo said:
So what equation could you use to plot theoretical values of Vout / Vin ?
Are you familiar with complex number arithmetic? With the representation of impedance using complex numbers? I think that is necessary to understand this without a tremendous amount of work.

Do you know about simple circuit analysis, like voltage dividers?

This is important information for us to know to help appropriately.
 
  • #5
Khan Academy has some really good tutorials on these subjects.
 

Related to Visualizing Series Bandpass Filters: A Graphical Approach

What is a series bandpass filter graph?

A series bandpass filter graph is a graphical representation of the frequency response of a series bandpass filter. It shows the amplitude of the output signal as a function of frequency, with a peak at the center frequency of the filter.

How does a series bandpass filter work?

A series bandpass filter works by allowing a specific range of frequencies, known as the passband, to pass through while attenuating all other frequencies. It consists of a series of inductors and capacitors that create a resonant circuit, which allows only a narrow band of frequencies to pass through.

What is the purpose of a series bandpass filter?

The purpose of a series bandpass filter is to selectively filter out unwanted frequencies and allow only a specific range of frequencies to pass through. This is useful in applications such as audio signal processing, radio communication, and electronic instrumentation.

How is the center frequency of a series bandpass filter determined?

The center frequency of a series bandpass filter is determined by the values of the inductors and capacitors used in the circuit. It is calculated using the formula fc = 1/(2π√(LC)), where fc is the center frequency, L is the inductance, and C is the capacitance.

What factors affect the performance of a series bandpass filter?

The performance of a series bandpass filter can be affected by several factors, including the quality of the components used, the design and construction of the filter, and external factors such as temperature and electromagnetic interference. The bandwidth and center frequency can also be adjusted by changing the values of the inductors and capacitors.

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