Table of Contents

Today, one or more opamps are housed in a single IC package of some sort. Hobbyists continue to prefer the DIP form of the IC, due to their size for ease of use.

For a painless introduction to opamps, the book titled “IC User's Casebook” by Joseph J. Carr is excellent (ISBN 0-672-22488-7). This book is old (1990) now, but continues to provide a cheap and excellent introduction to opamps. Books like these can be purchased economically online through places like www.abebooks.com.

Chapter 2 describes “The Ideal Operational Amplifier” and begins with a list of ideal opamp properties:

- Infinite open loop
*voltage*gain - Infinite input impedance
- Zero output impedance
- Zero noise contribution
- Zero DC output offset
- Infinite bandwidth

The amplifier shown at right is an opamp amplifier in the inverting configuration. The schematic does not show the power going into the opamp. So assume that +/-15 volts or similar are being applied to the opamp U1.

The non-inverting input (+) of the opamp is tied directly to the ground (which is midway between the two power rails). While the ideal opamp draws no input current, our real opamp will of course have a small amount of bias current flowing in the inputs, including the non-inverting input.

The gain of this amplifier is configured by R1 and R2:

The negative sign simply indicates that the output signal is 180 degrees out of phase with the input signal.

The output voltage is:

To tailor the upper frequency response, you can add a feedback capacitor like the one shown at right. To produce a cutoff frequency f, use the formula:

You can also use the online filter calculator. Plug in the value of and your cutoff frequency f, then compute the capacitance required.

To add a low frequency cutoff to the amplifier stage, simply insert another capacitor in series with input resistor , and apply the online filter calculator.

Supply the resistance and the lower cutoff frequency f, to compute .

The example shown at right uses AC coupling and has an upper cutoff frequency. The AC coupling capacitor is chosen to tailor the low frequency cutoff in this amplifier as well.

This circuit is designed with a gain of 20, a lower cutoff frequency of 300 Hz, and an upper cutoff frequency of 3000 Hz (frequency range of a telephone circuit).

The gain is computed from:

which is:

The upper frequency cutoff was chosen to be 3000 Hz, calculating C1 from:

To choose capacitor , compute:

To outline a complete design procedure, we must take into account the output impedance of the previous stage. In the previous example, we simply used an ideal voltage source (with zero source resistance). Otherwise, how do we choose and ? We know how to choose the ratio to arrive at a particular gain, but how do we choose the individual resistances?

We must know the source resistance. The design rule is that the input impedance of the
amplifier must be much greater than the source resistance. The rule of thumb for “much greater” is that it
must be *at least ten times* as great.

So if the output impedance of the previous stage is known to be approximately 1k ohms, then our amplifier must have an input impedance of at least ten times that, or no less than 10k ohms.

Knowing all this, the general design procedure is this:

- Determine the output impedance of the prior stage (source impedance).
- Determine the input impedance of the amplifier to be at least ten times the source impedance.
- If the source resistance is 100 ohms or less, try 10k ohms for . If the calculated feedback resistor is too large for the required gain, this value may be reduced somewhat. Generally speaking the calculated value of or 10k, whichever is the higher, is used.
- Determine the amount of gain required. In general, a single stage should have a gain not exceeding 500 (use multiple opamps for greater gain). Some low cost opamps should not be operated above a gain of 200.
- Determine the frequency response of the amplifier stage (the frequency at which the gain drops to unity). The minim gain bandwidth product is computed as . Make sure your chosen opamp is able to support this.
- Select your opamp meeting the gain and the GBP required, along with other factors like cost, availability etc.
- Choose the feedback resistor . If the value of is too large (10-20 Megohms is about the limit), then choose a lower and repeat. Note that must be low enough to satisfy the bias current of the opamp.
- To limit the stage's upper frequency response, calculate the shunting capacitor value ( above).
- If the stage is to be AC coupled, or requires a low frequency cutoff, then compute the coupling capacitor as done for above.

When choosing components, refer to the standard capacitor values chart or the standard resistor calculator.

The non-inverting amplifier is very similar to the inverting amplifier, except that the input has moved to the non-inverting input of the opamp, and resistor is grounded.

The output voltage is:

The above represents the input impedance of an *ideal* opamp. Your opamp, will have
a high input impedance that depends upon the part chosen.

To design the upper frequency cutoff response, you use feedback capacitor . To produce a cutoff frequency f, use the formula:

You can also use the online filter calculator. Plug in the value of and your cutoff frequency f, then compute the capacitance required.

This amplifier does not use an input coupling capacitor, implying that it is a DC coupled design. The AC non-inverting design procedure is outlined later on.

The DC coupled non-inverting amplifier design procedure is as follows:

- Select a trial value for resistor , chosen usually to have a value between 100 to 5000 ohms.
- Compute , where A is the required gain of the stage.
- If the calculated value of R_2 is not close enough to a readily available standard part value, try other values for R_1 and repeat.

AC coupling a non-inverting amplifier changes a couple of things in the design:

- There is now a chosen and finite
*input impedance*(effectively ). - There is now a implied
*high pass filter*added ( and )

The input impedance is the near infinite resistance in the non-inverting input in parallel with resistor . In practical terms, you can simply assume:

The high frequency cutoff is computed by considering and as before. Enter and the desired cutoff frequency f into the online RC filter calculator to compute the value needed for the shunting capacitor .

The low frequency cutoff is calculated by applying coupling capacitor in combination with input resistor . Using the online RC filter calculator, enter the resistance for and the desired low cutoff frequency f to calculate the required capacitance for .

The initial steps are identical with the DC procedure. We simply add steps for the input impedance and the low frequency cutoff:

- Select a trial value for resistor , usually chosen to have a value between 100 to 5000 ohms.
- Compute , where A is the required gain of the stage.
- If the calculated value of R_2 is not close enough to a readily available standard part value, try other values for R_1 and repeat.
- Choose such that it is
*at least ten times*the source resistance of the prior stage. - Choose coupling capacitor based upon the low frequency cutoff design parameter. Enter the cutoff frequency f and into the online RC filter calculator to compute capacitance for .

When choosing components, refer to the standard capacitor values chart or the standard resistor calculator.

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