The simplest bandpass filters are LC filters - they use inductors and capacitors (although there are always some additional resistors in the circuit that affect operation).
These components can be connected in series or parallel, and the resulting circuits are called series resonant circuits and parallel resonant circuits, respectively. The word resonance is used because these circuits respond to specific frequencies, just like the strings on a violin or guitar. Therefore, they are often referred to as tuning circuits.
This shows some examples of these circuits connected in different ways. The resonant frequency of both series and parallel circuits is due to the resistance effect, where XL of the inductor is equal to Xc of the capacitor. We can obtain the resonance frequency by solving this equation
Where f is frequency, L is inductance, C is capacitance, representing frequency:
In a parallel tuned circuit, capacitors and inductors are connected in parallel, so they have the same voltage. At the resonance frequency, we also have that their reactants are equal. According to Ohm's Law of AC circuits, if inductors and capacitors have the same voltage and reactance, they must also have the same current. So they all have the same current. But because one of the currents causes the voltage to advance by 90 "and the other current causes the voltage to lag by 90", they are 180 "apart. Therefore, the direction of the currents is opposite, one rising and the other falling. Therefore, the current in the wire leading to the secondary tuning circuit must be zero. Because the external current entering the tuning circuit is zero, the circuit behaves like an open circuit (with voltage but no current passing through).
The opposite situation occurs in a series resonant (also known as a series resonant device) circuit. Here, capacitors and inductors are connected in series, so the current is the same. This time, the voltage on one electrode guides the current, while the voltage on the other electrode lags behind the current by 90 ". Therefore, these two voltages are 180 inches apart. At resonance (another way of saying 'at resonance frequency'), their reactants are equal, so their voltages are equal, but opposite. Therefore, the total voltage of the entire series circuit is zero, even if there is current passing through. Therefore, the behavior of the circuit is like a short circuit (there is also current, but no voltage passing through).
Therefore, we have formed the following empirical rules:
During resonance, the parallel tuned circuit exhibits an open circuit.
During resonance, the series resonant circuit exhibits a short circuit.
At other frequencies, both circuits have a certain impedance. Approaching the resonant frequency, the circuit is not completely open (for parallel tuning) or short (for series tuning), but still very close. The further away from the resonant frequency, the smaller the circuit, and there may be open or short circuits.
Both of these circuits can serve as selective filters, allowing certain frequencies to pass through and preventing others from passing through. They can connect tuning circuits between two basic directions, such as (a) and (b) (in which case the signal will be shorter depending on the impedance of the circuit), or a signal must pass through an LC circuit from input to output as shown in (c) and (d) (in which case it will more or less pass through depending on the impedance of the circuit).
Taking circuit (a) as an example. During resonance, the parallel tuned circuit exhibits an open circuit, with most of the input signal directly reaching the output through resistors. According to the different output loads, there may be current in the series resistor, so there may be voltage loss, but we can ignore it. However, apart from resonance, the tuning circuit is no longer open; It causes the increased current to pass through the series resistor, resulting in an increase in voltage drop. The further away from resonance, the greater the decrease and the smaller the output voltage.
If we keep the input voltage constant but change the frequency, and then plot the relationship between the output voltage and frequency, we obtain a graph similar to Figure (a). We see that the peak of the output appears at the resonance frequency and there is a decrease on both sides. There is indeed a frequency band passing near the resonance, while the frequency far away from the resonance is reduced (although not completely stopped). Because there is a frequency band that can pass through, it is called a bandpass filter. The circuit (c) in the figure is also a bandpass filter; Due to the fact that the series resonant circuit is short circuited at the lightning point, the frequency of resonance passes through (and near), while the frequency decreases further away because the series resonant circuit now has some reactance.
Circuits (b) and (d) do the opposite thing - they stop signaling at resonance; Circuit (b) is achieved by shortening the signal, while circuit (d) is achieved by opening the path between the input and output. Even close to resonance, they will weaken the signal, so they will stop (or weaken) a frequency band as shown in Figure (b). Therefore, they are called band stop or band stop filters.
Please note the similarities between this and the RC low-pass or high pass filters discussed in the previous chapter. Although we are referring to the cutoff frequency here, the actual curve shows that 'cutoff' is actually a very slow decline. There is also a gradual change on both sides of the resonance frequency.