ECE 201 Lecture 14 Borja Peleato Frequency response 1 Impedance depends on w As we have seen the impedance of capacitors and inductors depends on the frequency of the currents and voltage Impedance is just a way to express the relationship between current and voltage If the impedance is low e g an inductor in DC or a capacitor at high frequencies you can have a lot of current with very small voltage If the impedance is high e g a capacitor in DC or an inductor at high frequencies you can have a high voltage with very small current Inductors and capacitors have complex impedances with different signs At the right frequency they can cancel each other 2 LC combinations 3 Frequency response Since impedances depend on the frequency of the inputs the voltages currents etc will also depend on w We are often interested in observing the gain ratio between the input and output magnitudes or the phase offset between the input and output as a function of w Two of the most basic examples are high and low pass filters 4 Band pass reject filters Read examples 10 14 10 16 from the text 5 Example You want to build a circuit to pick up NPR 920 AM and filter out as much as you can all other radio stations You have an antenna modeled as a voltage source and a capacitor and an amplifier modeled as an inductor and a buffer What should the other two elements in the circuit below be Hint You want signals at w 9 2 105 to get to the amplifier unchanged and attenuate all others Solution A Inductor 1 2 uH B Capacitor 0 2 uF 6 Frequency response for op amps This topic is for completeness purposes only The next slides will not be in the exam 7 Decibels dB Units like percentage increase times or kilo are independent of the concept being measured they just represent a transformation applied to the quantity before being reported e g kilo divide by 1000 Decibels are similar to the ones above Instead of reporting a quantity A we take the logarithm base 10 multiply by 10 or 20 and report the result in dB dB units are specially common for measuring gains or ratios between quantities not just in circuits but in many other disciplines as well When the ratio being measured is between amplitudes such as voltages or currents we multiply the log by 20 When the ratio is between powers we multiply the log by 10 So if Vout 100 Vin we say that the gain is 20 log Vout Vin 20 log 100 40 dB Similarly a 0 dB gain means that the input and output are equal and a 3 dB decrease in power consumption means that half as much power being consumed 8 Op amp frequency response Ideal op amps have infinite gain but real ones have a finite albeit very large gain denoted A0 As the frequency of the signal to be amplified increases the gain of the op amp decreases In DC the gain is maximum denoted A0 The frequency at which the gain is 3dB below the maximum is known as corner frequency The frequency at which the gain is 0 dB i e the output is just as big as the input is known as unity gain frequency 9 10 Amplifier circuits The frequency varying gain of the op amp affects the gain of the circuits where it is included For example in lecture 24 we studied the effect of non infinite gain in the inverting amplifier We saw that 11 Bandwidth vs gain trade off 12
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