Fig 1. The standard Howland Current Pump (HCP) is a current source that can generate both positive and negative current.
Fig 2. Adding a boost circuit to an HCP design allows for higher output current capability, creating a “power HCP.”
Fig 3. Using HCPs and power HCPs in place of operational transconductance amplifiers (OTAs) in a standard simulated inductor design creates a simulated inductor that can handle 1 A RMS and is tunable by adjusting the gain of U3.
Simulated inductors are useful in a variety of applications, including audio equalizers and filters. While it is easy to find published designs that handle currents of a few milliamps, however, it can be useful (especially in the prototyping of passive crossovers) to have a floating inductor that is both easily tuned and can handle larger currents, up to 1 A RMS.
Two well-documented textbook approaches for simulated floating inductor design are the genesis of numerous variants. One approach uses op amps wired as generalized impedance converters (GICs) and the other uses operational transconductance amplifier ICs (OTAs) wired as gyrators. Each approach has drawbacks.
The first textbook approach requires the back-to-back connection of two GICs, which involves some component-matching requirements. Changing the inductor value in this approach thus requires a bothersome replacement of matched components.
One drawback to the second textbook approach is that there are few choices for commercial OTA ICs, which constrains the designer. Further, the choices that are available are very low-current devices. For example, the LM13700 is a popular OTA but its transconductance output delivers less than 1 mA.
This makes the commercial OTA approach impractical for power applications. It is possible, however, to get around both the availability and current limitations of an OTA-centric topology by using high-current Howland Current Pumps (HCPs) instead of OTA ICs.
The standard textbook HCP, known as an Improved HCP when R4 > 0, uses a conventional op amp and requires the ratio R1/R2 to equal R5/(R3 + R4) as precisely as possible (Fig. 1). (For a good background on HCPs, see National Semiconductor Application Note 1515, “A Comprehensive Study of the Howland Current Pump,” by Robert Pease.) The HCP’s transconductance (G) is given by G = (R2/R1) × (1/R3) and with R4 = 0 and the other values shown, G = 1 × 10–6 A/V. While there is no a priori limitation on the value of G, the output current capability of the HCP is limited by that of the op amp used.
To enable higher-current operation, equip the HCP with a standard booster stage. This “power HCP” circuit uses a standard op amp (such as the TL074) and with the values shown has transconductance G = 0.1 A/V (Fig. 2). Because HCPs are current sources, though, they can get fidgety when presented with high-impedance loads. The 47R-15p-47p network in the design bypasses the HCP action at higher frequencies and improves the circuit’s stability with light loads.
You can now substitute an HCP (H2) and two power HCPs (H1, H3) for OTA ICs in a fairly canonical OTA-centric floating inductor topology (Fig. 3). The circuit provides the equivalent of a floating inductor with value given by the standard textbook formula L = C/(G1 × G2), where G1 is the transconductance of H1 and H3 and G2 is the transconductance of H2. With the component values shown, L = 1 µF/(1 × 10–7) = 10H. The simulated inductor of 10H has an output current capability of 1 A RMS.
The FET-input buffer stage (U3) is present to avoid the loading of capacitor C, which needs to work with microampere-level currents. By making U3 a variable-gain stage you can tune the simulated inductor to the value you desire. Setting the gain of U3 to A causes the capacitor C to appear smaller in the circuit (CEquivalent = C/A), reducing the simulated value L in proportion.
While this circuit can be used in applications where one end of the “inductor” is connected to ground, it is not advisable because its performance in that configuration is inferior to simpler, dedicated grounded-inductor designs. The design’s advantages really come to the fore in floating usage.