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Design Ideas |
The circuit in
Figure 1 provides programmable simulated inductance with 8-bit
resolution, without the use of inductive components. The circuit uses the
reactance of capacitor C1 to form a programmable gyrator. Possible
applications for the converter include programmable filters, generators,
equalizers, digital LCR meters and bridges, and tank circuits. The circuit uses
a multiplying D/A converter (MDAC), three op amps, four resistors, and one
capacitor.
The simulated inductance is independent of the tolerance of the MDAC's R-2R ladder resistances, provided that a good ratio match exists between the R-2R values and the MDAC's internal feedback resistor. Op amp IC1 and the combination of op amp IC2 and MDAC IC4 provide the simulation of the programmable lossy inductor, LEQ. The lossiness comes from the parasitic resistance, REQ. The MDAC is in the feedback loop of op amp IC2. The signal from IC2 feeds the MDAC's internal feedback resistor. The simulated inductance, LEQ, is proportional to the digital input code.
The third op amp, IC3, compensates for the parasitic resistance, REQ, thereby improving the quality factor, Q, of the simulated inductance. The equivalent impedance, ZEQ, between terminals 1 and 2 comprises:
GEQ represents the lossy parallel conductance. To obtain high Q, you must null or minimize this term. The relationship R1•R4=R2•R3 provides the minimum value of GEQ. For best results, R1 through R4 should have tight tolerances. For high stability, the positive term in Equation 2 must have a slightly higher value (0.05 to 0.1%) than the negative term. This requirement causes slight degradation of Q, but it is a necessary compromise. With the component values in Figure 1, the circuit simulates inductances from approximately 3 to 800 mH as the input code ranges from 00000001 to 11111111 (zero code is prohibited).
You can easily change the range of LEQ by varying the values of C1 or R1 through R4. The parasitic shunt resistance, REQ, is on the order of 100 k[ohm]; you can further increase it by fine-tuning resistor R2. You must also take a couple of design issues into consideration. The accuracy of the simulated inductance, LEQ, depends heavily on the dynamic performance of the MDAC and op amps. The circuit is well-suited for low, audio-frequency applications. When the frequency ranges beyond 100 kHz, the accuracy of LEQ degrades. You also must limit the signal level to ensure that the op amps operate in their linear range.
The LF347 quad op amp is a good choice for the converter due to its high input impedance, low distortion, and good dynamic performance. If dynamic range is an important consideration, the LM6118/6218 or LM6361 families are a good choice. The MDAC is the µP-compatible, 8-bit DAC-0830; you can upgrade to 10- or 12-bit resolution by using the DAC-10xx or DAC-12xx families, respectively. You could combine this circuit with a differential programmable impedance to provide a wide spectrum of mixed-signal-processing configurations (Reference 1). (DI #1930)