Electronic Design

# What Color Was George Washington’s White Horse?

You really have to hate questions like this. It’s a typical pub quiz question that’s most likely going to cause you to buy a round. You don’t have a clue what the answer really is, and you’re pretty sure the answer isn’t white. But there’s the slightest chance the answer is white, so ignoring this possibility could make you look stupid.

Do you guess and let your friend tell an embellished story? Or do you just buy the round and get it over with? Or, if you prefer, you can counter with your drink-winning pub question: how many inputs does a differential amplifier have?

Start Counting

Your impulse answer may be two, and in a way you would be right. Figure 1 shows an ideal differential amplifier. Equation 1 defines the relationship between the inputs and the outputs for an ideal differential amplifier:

So far the input count is two.

A real-world amplifier will have a very significant term. It is the common-mode gain of the inputs. This increases the complexity of the equation to:

Common-mode rejection ratio (CMRR) is the ratio of these two gains (CMRR = Gaind/Gainc). It provides the equivalent differential input for a specific common-mode input. CMRR is a specification found for an amplifier in its datasheet. The input count is now up to four.

Real amplifiers must have power connections, and those connections are inputs (Fig. 2). These inputs will also affect the output:

Power-supply rejection ratio (PSRR) is the ratio of the differential gain and power-supply gain (PSRR = Gaind/Gainp). It determines how much of the power supply ends up in the output.

To reduce the amount of power-supply ripple getting into your amplifier’s output, reduce the ripple at the supply or get an amplifier with a higher PSRR. Generally, amplifiers with good CMRR also have good PSRR. By the way, the input count is now six.

A practical amp will have an offset error and noise. These inputs will also affect the output:

The noise is referred to the input (rti), as is the offset voltage. These terms are determined by the amplifier’s design and will have a big influence on cost. They also put the input count at eight.

Of course, all these gain values are a function of frequency:

So frequency is an input too, and the count is nine.

Noise is a function of temperature, and the other gains can have temperature dependencies:

With temperature, the count is up to 10.

The Final Count

So I end up with a count of 10—maybe 11 or 12 if you separate 1/f noise and process (popcorn) noise from the thermal noise. All of these effects can be found in your amplifier’s datasheet. If you aren’t getting the performance you wanted, chances are you have overlooked one of these parameters.

The same goes for a differential input analog-to-digital converter (ADC). An ADC is just an amplifier with a digital output. If you can think of any other inputs, please contact me. I would hate be “one upped” next time I am in a pub.

Postscript

George Washington’s horse was gray, like the old mare. Grays are born with dark skin and gray hair that often turns pure white with age. White horses are born with white hair and have pink skin, the same color as baby rats. Now someone please order me a Guinness.