Components like inductors and capacitors constitute an integral part of filters and oscillators used for communication and biomedical applications. A common problem intrinsic to passive inductors is their enormous size as their value increases. Efforts have been made to actively simulate such passive devices.
In biomedical applications, various filter and oscillator structures need to operate at very low frequencies (less than 50 Hz). Brain-wave frequencies are typically in the low-Hertz range (e.g., Delta: 0-4 Hz, Theta: 4-8 Hz, Alpha: 8-12 Hz, Beta1: 14-16 Hz, Beta2: 16-20 Hz, etc.). Hence, very high-value inductors and capacitors are often required when designing devices such as EEG instruments.
To achieve such high values (e.g., greater than 1000 H) using conventional impedance simulating circuits, very high-value resistors would be needed. This is not feasible for integrated circuit technology.
An economical and versatile circuit is presented here that can simulate high-value, grounded inductors. It can also function like an impedance multiplier/scalar. In addition, this arrangement provides the added advantage of tunability, since a wide range of values can be achieved without disturbing the design. The design, as shown in Figure 1, is robust and economical. It uses a commonly available dual transconductance op amp (OTA) chip from National Semiconductor (LM13600) and off-the-shelf µA741 op amps. With GM as the OTA transconductance, the input impedance of the circuit is:
VIN/IIN = Z5/(GM1GM2Z3Z4)
where ZI can be resistors or capacitors and
where IB is the OTA bias current.
Since GM can be varied theoretically up to six decades (per datasheet), the overall impedance function can be varied up to 12 decades. This yields a possible multiplication factor of nearly 2.5 × 1011.
Figure 2 shows a bandpass filter (BPF), using this scheme, which is very useful when designing EEG instruments. Though the BPF has been configured to pass Theta-type waves (associated with lifelike imagination, particularly dominant in children), the intuitive use of OTA for design makes it possible to program the filter for any wave frequency by simply tuning the bias current.
With the component values shown, the filter yields a center frequency of approximately 7 Hz and a Q factor of about one.
The OTA amps are biased with 1-µA currents. (Widlar-type current mirrors are capable of supplying such low currents while using nominal resistor values). It should be mentioned that, although the scheme synthesizes grounded impedances, the circuit can easily be converted into a floating structure using only an additional OTA and an on-chip buffer (This grounded-to-floating conversion method is attributed to Prof. Raj Senani).