Electronic Design

# Resistor-less Sinusoid Generator Also Measures Capacitance

Current-mode (CM) active elements provide the advantages of high slew rate and wide bandwidth. One important CM building block is the second-generation current-controlled conveyor (CCCII) (Fig. 1).

Various circuits can be built from CCCIIs, including universal filters, oscillators, and inductor simulators, with the distinct feature that they do not use external linear resistors. Rather, these circuits utilize the parasitic resistance at terminal X of the CCCII, and that resistance is bias-current controllable.

Using two CCCIIs as core components allows the creation of a dual-current-controlled current differencing buffered amplifier (DCC-CDBA). The DCC-CDBA, in turn, can be configured to create a variable-frequency oscillator (Fig. 2) that is tunable by varying bias current IB1 or IB2. The condition for oscillation (CO) of this circuit is such that the use of a known variable capacitance at C1 provides a means of measuring an unknown capacitance at C2. With the input Y grounded, the following equations characterize the CCCII:

IY = 0
IZ+ = IX
IZ– = –IX
VX = VY + IXRX

The parasitic resistance RX depends both on the thermal voltage at that input (VT) and the bias current (IB). In particular:

RX = VT/2IB

Connected in the DCC-CDBA configuration, the circuit has:

VP = IPRP
VN = INRN
IZ = IP – IN
VW = VZ

where RP and RN are the parasitic resistances at terminals P and N, respectively. In the Laplace domain, circuit analysis shows that:

s2C1C2RPRN + s(C2RN + C1RP – C1RN) + 1 = 0

This circuit will act as an oscillator when:

C2RN + C1RP – C1RN = 0

or:

The frequency of oscillation is:

Substituting for the bias-current and thermal voltage relationships of the parasitic resistances yields:

and:

If the ratio of IB2 to IB1 is fixed at a constant value k, the condition of oscillation becomes (C2/C1) = 1 – k, or C2 = C1(1 – k). Thus, the unknown capacitance C2 can be found by varying the known capacitance C1 until the circuit is at the threshold of oscillation.

The proposed circuit here has a structure that’s very similar to that of the oscillator circuit proposed by Koskal et al in \\[1\\]. However, a careful look reveals the most important difference between the circuits. While the circuit in \\[1\\] uses CC-CDBA, which has ideally equal parasitic resistances, the circuit here uses DCC-CDBA, which can have different parasitic resistances at terminal p and n by means of different bias currents.

The circuit in Fig. 1(a) of \\[1\\] completely relies on the slight non-ideal differences between the parasitic resistances RP and RN and causes (or may cause) the startup of oscillations. In particular, this circuit would completely fail to oscillate when RP is slightly greater than RN, which is quite possible due to random mismatches. The authors then ingeniously use an external resistor at terminal n, thereby increasing the effective n terminal resistance.

A more reliable “resistor-less” solution with electronic tunability is provided here, wherein both RP and RN are tunable by two different bias currents and would then easily satisfy the CO for given unequal capacitor values.

REFERENCE
1. M. Koskal, M. Sagabas and H. Sedef, “An electronically tunable oscillator using a single active device and two capacitors,” Journal of Circuits, Systems and Computers, vol. 17, no. 5, pp. 885-891, 2008.