Third Order Universal Filter Using Single Operational Transresistance Amplifier

Table 2

Condition of realization of each filter.

Filter response	Condition
LPF	𝑅𝑐𝑅a2+𝑅a1𝑅𝑏=𝑅a2𝑅a1, 𝐶a2𝑅a2+𝐶b2𝑅𝑏+𝐶a2𝑅a1=𝐶b2𝑅a1
HPF	𝐶a1+𝐶a2=𝐶b2, 𝐶a1𝐶a2𝑅a2+𝐶a1𝐶b2𝑅𝑏+𝐶a2𝐶b2𝑅𝑏=𝐶b2𝐶a2𝑅a2
APF	𝐶b1𝑅a1=𝐶𝑐𝑅𝑐,−(𝐶a2𝑅a2+𝐶b2𝑅𝑏+𝐶a1𝑅a1−𝐶b1𝑅a1−𝐶b2𝑅a1)=𝐶𝑑𝑅𝑑+𝐶𝑐𝑅𝑐+𝐶𝑑𝑅𝑐+𝐶b2𝑅𝑏,𝐶b2𝑅𝑏𝐶a2𝑅a2+𝐶a2𝑅a1𝐶b2𝑅𝑏−𝐶b1𝑅a1𝐶a2𝑅a2−𝐶b1𝑅a1𝐶a2𝑅𝑏=𝐶𝑐𝑅𝑐𝐶𝑑𝑅𝑑+𝐶b2𝑅𝑏𝐶𝑑𝑅𝑑+𝐶b2𝑅𝑏𝐶𝑐𝑅𝑐−𝐶b2𝑅𝑏𝐶𝑑𝑅𝑐
BPF	𝐶a2=𝐶b2
NF	𝐶a1𝑅a1=𝐶𝑐𝑅𝑐,𝐶𝑑𝑅𝑑+𝐶b2𝑅𝑏+𝐶𝑐𝑅𝑐−𝐶𝑑𝑅𝑐=𝐶a2𝑅a2+𝐶b2𝑅𝑏+𝐶a1𝑅a1+𝐶a2𝑅a1−𝐶b2𝑅a1,𝐶b2𝑅𝑏𝐶a2𝑅a2+𝐶a1𝑅a1𝐶a2𝑅a2+𝐶a1𝑅a1𝐶b2𝑅𝑏+𝐶b2𝑅a1𝐶a2𝑅𝑏=𝐶b2𝑅a1𝐶a2𝑅a2