Opamp Notes

The venerable 741 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.

Book: IC User's Casebook

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.

The Ideal Opamp

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

  1. Infinite open loop voltage gain
  2. Infinite input impedance
  3. Zero output impedance
  4. Zero noise contribution
  5. Zero DC output offset
  6. Infinite bandwidth

Inverting Amplifier

Inverting Amplifier 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.

Gain

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

A=\frac {-R2} {R1}

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

Output Voltage

The output voltage V_o is:

V_o = A \cdot V_{in}

Input Impedance

R_{in} = R_1

Frequency Tailoring

Frequency tailored inverting amplifier

To tailor the upper frequency response, you can add a feedback capacitor C_1 like the one shown at right. To produce a cutoff frequency f, use the formula:

C_1=\frac {1} {2 \pi \cdot R_2 \cdot f}

You can also use the online filter calculator. Plug in the value of R_2 and your cutoff frequency f, then compute the capacitance required.

To add a low frequency cutoff to the amplifier stage, simply insert another capacitor C_2 in series with input resistor R_1, and apply the online filter calculator.

Supply the resistance R_1 and the lower cutoff frequency f, to compute C_1.

Example

Inverting Amplifier Example

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).

Gain

The gain is computed from:

A = \frac {-R_2} {R_1}

which is:

A = \frac {-200k} {10k} = -20

Upper Frequency Cutoff

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

C_1 = \frac {1} { 2 \pi \cdot f \cdot R_2 }

= \frac {1} {2 \pi \cdot 3000 \cdot 200000 }

= 265.25E-12

C_1 = 270 pf

Lower Frequency Cutoff

To choose capacitor C_2, compute:

C_2 = \frac {1} { 2 \pi \cdot f \cdot R_1 }

= \frac {1} { 2 \pi \cdot 300 \cdot 10000 }

= 53.0E-9

C_2 = 0.05 uF

Design Procedure

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 R_1 and R_2? 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:

  1. Determine the output impedance of the prior stage (source impedance).
  2. Determine the input impedance of the amplifier to be at least ten times the source impedance.
  3. If the source resistance is 100 ohms or less, try 10k ohms for R_1. If the calculated feedback resistor is too large for the required gain, this value may be reduced somewhat. Generally speaking the calculated value of R_1 or 10k, whichever is the higher, is used.
  4. 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.
  5. 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 GBP = A \cdot f. Make sure your chosen opamp is able to support this.
  6. Select your opamp meeting the gain and the GBP required, along with other factors like cost, availability etc.
  7. Choose the feedback resistor R_2 = |A| \cdot R_1. If the value of R_2 is too large (10-20 Megohms is about the limit), then choose a lower R_1 and repeat. Note that R_2 must be low enough to satisfy the bias current of the opamp.
  8. To limit the stage's upper frequency response, calculate the shunting capacitor value (C_1 above).
  9. If the stage is to be AC coupled, or requires a low frequency cutoff, then compute the coupling capacitor as done for C_2 above.

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

Non-Inverting Amplifier

Non-inverting amplifier

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 R_1 is grounded.

Gain

A = \frac {R_2} { R_1 } + 1

Output Voltage

The output voltage V_o is:

V_o = A \cdot V_{in}

Input Impedance

R_{in} = \infty

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

Upper Frequency Cutoff

To design the upper frequency cutoff response, you use feedback capacitor C_1. To produce a cutoff frequency f, use the formula:

C_1=\frac {1} {2 \pi \cdot R_2 \cdot f}

You can also use the online filter calculator. Plug in the value of R_2 and your cutoff frequency f, then compute the capacitance required.

DC Non-Inverting Design Procedure

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:

  1. Select a trial value for resistor R_1, chosen usually to have a value between 100 to 5000 ohms.
  2. Compute R_2 = R_1 \cdot ( A - 1 ), where A is the required gain of the stage.
  3. 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 Coupled Non-Inverting Amplifier

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

  • There is now a chosen and finite input impedance (effectively R_3).
  • There is now a implied high pass filter added (C_2 and R_3)

Input Impedance

The input impedance is the near infinite resistance in the non-inverting input in parallel with resistor R_3. In practical terms, you can simply assume:

R_{in} = R_3

High Frequency Cutoff

The high frequency cutoff is computed by considering C_1 and R_2 as before. Enter R_2 and the desired cutoff frequency f into the online RC filter calculator to compute the value needed for the shunting capacitor C_1.

Low Frequency Cutoff

The low frequency cutoff is calculated by applying coupling capacitor C_2 in combination with input resistor R_3. Using the online RC filter calculator, enter the resistance for R_3 and the desired low cutoff frequency f to calculate the required capacitance for C_2.

Design Procedure

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

  1. Select a trial value for resistor R_1, usually chosen to have a value between 100 to 5000 ohms.
  2. Compute R_2 = R_1 \cdot ( A - 1 ), where A is the required gain of the stage.
  3. 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.
  4. Choose R_3 such that it is at least ten times the source resistance of the prior stage.
  5. Choose coupling capacitor C_3 based upon the low frequency cutoff design parameter. Enter the cutoff frequency f and R_3 into the online RC filter calculator to compute capacitance for C_3.

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

opamps.txt · Last modified: 2012/12/10 14:42 by ve3wwg
 
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