A silly simple and ubiquitous circuit network is a variable resistance consisting of the series connection of a manually adjusted rheostat-connected pot and fixed resistor shown in Figure 1.

Figure 1. |
Classic variable resistance with the seriesconnection of a manually adjusted rheostat-connected pot and a fixed resistor. |

The availability of pots and resistors spanning ohms to megohms makes optimum choices of Figure 1’s component values obvious and easy. But if an application calls for using a digital potentiometer (Dpot), the situation gets more – ahem – interesting.

Dpots are only available in a relatively narrow range of resistance compared to manual pots. They also suffer from larger wiper resistances and wider tolerances. These limitations make them a dubious choice for implementing precision rheostats if Figure 1’s classic passive topology is solely relied upon. Figure 2 offers an active and more Dpot-friendly alternative.

Figure 2. |
Synthetic Dpot evades problems using FET shunt, precision fixed resistors, and op-amp. |

Here’s how it works.

Despite the fact we’re implementing a variable resistance, Dpot U1 is operated in potentiometer mode. So, its resistance tolerance (±20% for the MCP41xx series) has little negative effect. The precision of R_{S }and R_{P} dominate. Likewise, Dpot wiper resistance is rendered purely academic by the pA input current and T ohms input impedance of A1. A1 and Q1 are connected as a programmable current source. Its output is proportional to the V_{A} – V_{B} voltage differential, thus forming a precise programmable resistance. This relationship makes current I_{AB} linearly proportional to N.

Design equations are for appropriate resistances starting from specified R_{AB}, R_{MAX}, and R_{MIN} are:

Figure 3 shows a typical design example for R_{MAX} = 20k, R_{MIN} = 1k.

Figure 3. |
Synthetic rheostat design example where R_{MAX }= 20k and R_{MIN} = 1k. |

Figure 4 plots R and current per (V_{A} – V_{B} volts) as functions of N.

Figure 4. |
Performance of Figure 3’s circuit with values shown, the linear relationshipbetween N and I _{AВ} conserves the Dpot’s limited 8-bit resolution. |

Note the accurately linear relationship between N and I_{AB} current which does a good job of conserving Dpot limited 8-bit resolution.

A question arises: What if the required R_{MAX} is larger than the R_{AB} resistance of available Dpots? Figure 5 offers a practical (although admittedly somewhat busy) solution that can easily implement an accurate R_{MAX} extending far into the multi-megohm range.

Figure 5. |
Two buffer amps remove R_{AB} from R_{MAX }equation, allowing for an R_{MAX} extending far into the megaohms. |

Another (stickier) question is: What happens if the polarity of V_{A} – V_{B} is subject to reversal? Figure 1 can accommodate this without a second thought, but it’s a significant problem for this design idea.

I’ll have to get back to you on that one!