1• Frequency responseECE 201: Lecture 14Borja PeleatoImpedance 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 other2LC combinations3Frequency 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 filters4Band pass/reject filters• Read examples 10.14-10.16 from the text5Example6You 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*105to get to the amplifier unchanged,and attenuate all others).Solution: A: Inductor 1.2 uH B: Capacitor 0.2 uFFrequency response for op amps• This topic is for completeness purposes only. The next slides will not be in the exam7Decibels (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 dBSimilarly, 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.8Op 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 frequency910Amplifier 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 11Bandwidth vs gain
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