Higher Physics – Unit 2 2.4Analogue Electronics

Op-Amp An op-amp has two inputs and one output. The symbol for an op-amp is: inverting input non-inverting input V S - V S VoVo V1V1 V2V2 The supply voltage may or may not be included in circuit diagrams.

An op-amp is used to increase the voltage of a signal. The frequency of the signal remains unchanged k k10k1M voltage gain frequency / Hz 100,000 An op-amp typically has a gain of about 100,000. Such a high gain is limited to a narrow range of frequencies.

Ideal Op-Amp An ideal op-amp has: infinite input resistance zero current no potential difference between inputs (both the same)

All applications we study have a feedback resistor. + - R1R1 VoVo V1V1 V2V2 RfRf Gain of the amplifier with feedback depends only on the size of input resistor and feedback resistor. Negative Feedback

0100 k k10k1M voltage gain frequency / Hz 100,000 An op-amp used with negative feedback, returns some of the output signal to the inverting input. This reduces the size of voltage gain, but it remains constant over a larger range of frequencies.

Inverting Mode Circuit + - R1R1 VoVo V1V1 RfRf 0 V The positive input (non-inverting input) voltage is connected to 0V when in the inverting mode.

Gain Formula Output Inverting Mode Non-Inverting Mode Input Signal Output Signal The negative sign means that input signal is inverted

Example Calculate the output voltage in the circuit shown. + - VoVo 400 mV 50 kΩ 0 V 2 kΩ

Experiment kΩ 1 kΩ +12V -12V VoVo V1V1 The size of V 1 is altered by varying resistor R V. V 1 and V o are recorded for various values of R V. RVRV

Results V 1 (volts)V o (volts)

Graph V 1 / volts V o / volts Conclusion Saturation occurs at +12 V and -12 V. Saturation is where the output voltage reaches the supply voltage V S. V o cannot exceed V S.

Saturation An op-amp cannot produce an output voltage greater than the supply voltage. When V o reaches V S, the op-amp is said to be saturated. *** It is NOT the voltage that is saturated. *** In practice, the op-amp becomes saturated at about 85% of the supply voltage.

Input SignalOutput Signal + V S - V S This type of output signal causes distortion of an audio signal. It does however produce a square wave from a sine wave. Square Waves

Example 1 An op-amp is connected as shown. + - VoVo 1 V 100 kΩ 0 V 10 kΩ +15 V -15 V (a)In what mode is the op-amp being used in this circuit? (b)Calculate the output voltage V o. (c)The input voltage is increased to 2 V. Calculate the new output voltage V o.

(a)Inverting Mode. (b) (c) greater than V S : op-amp saturated (85% of V S )

Purple Book Page 57 Q1, Q2 (a) + (c), Q5 (b) + (d) Page 58 Q1, Q2 (a) + (c), Q3 (b) + (d), Q4

Differential Mode When the op-amp is in differential mode, both inputs are used. Circuit + - R1R1 VoVo V1V1 RfRf 0 V R2R2 R3R3 V2V2 Resistor R 3 is usually chosen so that:

Formula The difference between the 2-inputs is amplified. Voltage gain in differential mode is The output voltage is calculated by:

Example Calculate the output voltage V o for the circuit shown kΩ VoVo 40 mV 50 kΩ 0 V 25 mV

Questions 1.Calculate V o for the circuits shown. 15 mV kΩ VoVo 40 mV 30 kΩ 80 mV kΩ VoVo 35 mV 50 kΩ (a)(b) 2.Calculate V for the circuits shown. V kΩ 0.4 V 30 mV 45 kΩ 80 mV kΩ 0.6 V V 60 kΩ (a)(b) V V V+0.06 V

Purple Book Page 60 Q1, Q2 (a), Q4 and Q6

Op-Amp and Wheatstone Bridge kΩ VoVo 20 kΩ 0 V 4 kΩ 2 kΩ 3 kΩ +12 V -12 V Calculate the output voltage V o.

Step 1 Calculate the size of V 1. 0 V 2 kΩ 4 kΩ +12 V V1V1 Step 2 Calculate the size of V 2. 0 V 3 kΩ +12 V V2V2

Step 3 Calculate V 0.

Question An op-amp with a gain of 40 is connected to a Wheatstone bridge circuit as shown. (a) What mode is the op-amp connected in the circuit? (b) Calculate V o when the resistance of the LDR is 4000 Ω. (c) The resistance of the LDR is changed to 3000 Ω. State what happens to the output voltage after this change. differential 12 v - TO VoVo 0 V 12 kΩ 18 kΩ 5400 Ω +12 V -12 V

kΩ VoVo 100 kΩ 0 V 75 kΩ 2900 Ω +12 V -12 V Question An op-amp connected to a Wheatstone bridge circuit is shown Ω Calculate the output voltage of the op-amp.

Transistor Output TURD – temperature up, resistance of thermistor goes down. Voltage across thermistor goes down.  V 1 goes down. V1V1 0 V +V S V2V V motor for cooling fan M VoVo

Consider the equation. When V 1 goes down, V o goes up. Transistor switches ON. Relay switches ON. Cooling motor switches ON.

Purple Book Page 62 - Q1, Q2 Page 63 – Q1