A reference circuit includes: (a) a first reference circuit having a reference signal and a .DELTA.V.sub.BE loop; and (b) a modification circuit using a first voltage to change a first current in the .DELTA.V.sub.BE loop of the first reference circuit. In one embodiment, the reference circuit is a voltage reference circuit. In some embodiments, the reference circuit can include a bandgap core circuit, which adds a V.sub.BE and a multiplied .DELTA.V.sub.BE, so that the output voltage of the reference circuit is a bandgap voltage. The reference circuit also can also include a modification circuit, which uses the output voltage (i.e. the reference signal) of the bandgap core circuit to change a current in the .DELTA.V.sub.BE loop. The .DELTA.V.sub.BE loop can be the portion of the circuit involved in generating the .DELTA.V.sub.BE voltage. Other embodiments are disclosed in this application.