Op-amp gain less than 1 (not negative)

Question

I want to attenuate a DC voltage by a fixed amount, e.g. to divide 4 V by 2 and get 2 V.

The divisor needs to be a ratio of two resistors, so I cannot use a simple voltage divider. I presumed I could easily do this using op-amps, but so far I haven't been successful. This is what I have attempted:

I have no negative voltages in my circuit, so I have connected V- to ground. I chose resistors according to the formula found here.

I expected the output to be 2 V in accordance with the gain formula, yet it isn't. I have simulated this with other op-amps and obtained similar results.

How can I make an op-amp have a gain < 1 without using a negative voltage? If this isn't possible, how else can I divide a voltage according to the exact ratio of two resistors?

The op-amp is powered by a 5 V regulator.

Answer 1

The arrangement you have there is a so-called inverting circuit - it wants to create a negative 2V output voltage, which it can't without a negative power supply.

Instead, try this arrangement:

^{simulate this circuit – Schematic created using CircuitLab}

A plain old voltage divider is used to cut the voltage in half, and this op-amp arrangement (known as a voltage follower or buffer) simply copies the voltage it sees on the + input.

Answer 2

The divisor needs to be a ratio of two resistors, so I cannot use a simple voltage divider.

Most likely you're looking for a voltage-controlled current source (VCCS). It can be configured so that output voltage is proportional to the simple ratio of a resistor to the reciprocal of transconductance of the VCCS.

^{simulate this circuit – Schematic created using CircuitLab}

The VCCS can be designed so that its transconductance is the reciprocal of a programming resistor value, e.g. as in an Improved Howland Current Source.

This achieves the ratio you want, in a non-inverting circuit, with two resistors directly participating.

Answer 3

Simply attenuate Rs:Rp to get 50% before the input Vin+ with unity gain.

Another way if saying this is use two resistor to divide the input in 2 then use the standard unity gain Op Amp config (with a negative feedback jumper loop to Vin-.) since the inverting gain is 0, the non-inverting gain is 1+|0|=1.

But to get down to 0V which is your negative supply, you need what's called a rail-to-rail Op Amp for both input rails and output rails.

You choose the value of R and tolerance.

Your design would require the output to go to -2V in order to get Vin- to be forced to match Vin+ so the input error is null. But because the output drive could not get less than 919 mV, it failed to reach it's target. It's a high gain error amplifier so the inputs must be satisfied for range and match to work with the correct feedback. This makes it a little harder when using a single supply, but not that hard.

Answer 4

You have wired your setup as an inverting opamp, but you have used the formula for a non-inverting opamp. If you plug the in the resistances, you get the expected 0.5 gain, but with an inverted output. If you followed this by a second inverting unity opamp, you would get the final result of an attenuated signal.

However, if you want to use a single non-inverting opamp, lets take the formula: Gain = 1 + Rf/Rin. See the 1. Thats a problem. This means that to get an attenuation one of Rf or Rin must have negative resistance, which means an active circuit, not something possible with a simple resistor.

Thats the maths, for a more intuitive understanding, opamps are amplifiers, the opamp is amplifying the input difference, which is retarded by the negative feedback to a controlled gain. In order to achieve an attenuation, that feedback needs to be inverted, applying feedback to increase the apparent strength of the input signal. The problem with that is you end up with an unstable oscillator topology as any noise is amplified in a loop instead.

Part of the problem in understanding your question is that a fixed attenuation circuit with one input and one output isn't going to solve your problem of (V1/V3-V2) if you view V2 and V3 as voltages and not resistors. You need a voltage controlled attenuator, and those are not trivial. However, you mention that their are only 4 values of (V3-V2). As such I would suggest you achieve your problem by selecting the value of (V3-V2) in the digital domain by having the switches wired as logic lines into a subtraction IC, and use that with a decoder to select the resistor to switch into the divider using a MOSFET.