Second-order Sallen-key Stages have Steep 40dB/decade roll-off than cascaded RC.Replication of RC Components and Amplifiers.Each RC stage can have a different Voltage Gain.Low-pass and High-pass stages can be Cascaded Together.First and Second-order Filter Designs can be Easily Cascaded Together.The use of a Non-inverting Amplifier to Increase Voltage Gain.Simplicity and Understanding of their Basic Design.The main advantages of the Sallen-key filter design are: Sallen-Key is one of the most common filter configurations for designing first-order (1 st-order) and second-order (2 nd-order) filters and as such is used as the basic building blocks for creating much higher order filters. One simple way to cascade together RC filter stages which do not interact or load each other to create higher-order filters (individual filter sections need not be identical) which can be easily tuned and designed to provide required voltage gain is to use Sallen-key Filter stages. But what if you wanted to design a 4 th or a 6 th-order filter, then the calculation of ten times the value of the previous components can be time consuming and complicated. The advantage of increasing the component values by a factor of 10 is that the resulting second-order filter produces a steeper roll-off of 40dB/decade than cascaded RC stages. That is R B = 10*R 1 and C B = C A/10 at the cut-off frequency. One way to overcome this problem for a passive filter design is to have the input impedance of the second RC stage at least 10 times greater than the output impedance of the first RC stage. So our voltage divider transfer function from above becomes:Ĭascading one RC filter stage with another (identical or different RC values), does not work very well because each successive stage loads the previous one and when more RC stages are added, the cut-off frequency point moves further away from the designed or required frequency. However, somewhere in between these two frequency extremes the capacitor has an impedance given by X C. Capacitive reactance is frequency dependant, that is at low frequencies ( ƒ ≅ 0) the capacitor behaves like an open circuit and blocks them.Īt very high frequencies ( ƒ ≅ ∞) the capacitor behaves like a short circuit and pass the signals directly to the output as V OUT = V IN. In an AC circuit, a capacitor has the property of capacitive reactance, X C but we can still analyse the RC circuit in the same way as we did with the resistor only circuits, the difference is that the impedance of the capacitor now depends on frequency.įor AC circuits and signals, capacitive reactance ( X C), is the opposition to alternating current flow through a capacitor measured in Ohm’s. So now we are analysing the RC circuit in the frequency domain, that is the part of the signal that depends on time. If we now change the input supply to an AC sinusoidal voltage, the characteristics of this simple RC circuit completely changes as the DC or constant part of the signal is blocked. In other words, capacitors block steady state DC voltages once charged. Therefore there is no current flowing through the resistor, R and no voltage drop developed across it, so no output voltage. Thus when a steady state DC supply is connected to V IN, the capacitor will be fully charged after 5 time constants (5T = 5RC) and in which time it draws no current from the supply. The Sallen and Key topology is an active filter design based around a single non-inverting operational amplifier and two resistors, thus creating a voltage-controlled voltage-source (VCVS) design with filter characteristics of, high input impedance, low output impedance and good stability, and as such allows individual Sallen-key filter sections to be cascaded together to produce much higher order filters.īut before we look at the design and operation of the Sallen-key filter, let’s first remind ourselves of the characteristics of a single resistor-capacitor, or RC network when subjected to a range of input frequencies. The advantage of using Sallen-Key Filter designs is that they are simple to implement and understand. The Sallen and Key Filter design is a second-order active filter topology which we can use as the basic building blocks for implementing higher order filter circuits, such as low-pass (LPF), high-pass (HPF) and band-pass (BPF) filter circuits.Īs we have seen in this filters section, electronic filters, either passive or active, are used in circuits where a signals amplitude is only required over a limited range of frequencies.
0 Comments
Leave a Reply. |