ECE4435 HomeworkPhysical Characteristics of Op-Amps1. An op-amp has the low-frequency open-loop gain A0=105. The op-amp is to be used in aninverting amplifier with a gain of −2000. (a) What is the required ratio RF/R1? [2040.8](b) For the value of RF/R1, how much larger is the input resistance than R1?[1.0204R1]2. An op-amp has the low-frequency open-loop gain A0=105.Theop-ampistobeusedina non-in verting amplifier. The theoretical gain is calculated assuming that the op-amp isideal. What is the highe st theoretical gain that gives an error between the theoretical gainand the actual gain that is less than 5%? [5263.2]3. At low frequencies, an op-amp has an open-loop gain A0=105andanopen-loopoutputresistance R0=150Ω. The op-amp is to be used in a non-inverting amplifier having avoltage gain of 200. If the amplifier is designed with the assumption that the op-amp is idealand the input resistance to the feedback network is to be 100 kΩ, calculate the actual gainof the circuit and its output resistance. [199.60, 0.29940 Ω]4. At low frequencies, an op-amp has an open-loop gain A0=105andanopen-loopoutputresistance R0= 150 Ω. The op-amp is to be used in an inverting amplifier having a voltagegain of −200. If the amplifier is designed with the assumption that the op-amp is ideal withan amplifier input resistance of 1 kΩ, calculate the actual gain of the circuit and its outputresistance. [−199.6, 0.301 Ω]5. An op-amp has the gain-bandwidth product fx=1.5 MHz. The op-amp is to be used in anon-inverting amplifier circuit. Calculate the highest gain that the amplifier can have if thehalf-pow er or −3 dB bandwidth is to be 30 kHz or greater. [−50]6. Two non-inverting op-amp amplifiers are operated in cascade. Each amplifier has a gain of20. If each op-amp has the gain-bandwidth product fx=1.5 MHz, calculate the half-poweror −3 dB bandwidth of the cascade amplifier. [48.3kHz]7. An op-amp has the gain-bandwidth product fx=1.5 MHz. Compare the bandwidths of aninverting and a non-inverting amplifier which use the op-amp if the dB values of the voltagegain magnitude A0fare 0 dB, 10 dB, 20 dB, and 30 dB. [Non-inverting: 1.5MHz,4.74 kHz,150 kHz, 47.4 kHz, Inverting: 750 kHz, 360 kHz, 136 kHz, 46 kHz]8. An op-amp has a dc gain A0=105and a gain bandwidth product fx=1.5MHz. Theop-ampisusedinaninvertingamplifier with the element values R1=1.5kΩ and RF=75kΩ.Calculate the dc gain of the amplifier, the upper cutoff frequency, and the value of theelements in the equivalent circuit for the input impedance. [−49.98, 29.4kHz,R2=0.75 Ω,L =7.96 mH]9. The op-amp in the preceding problem has an open-loop output resistance R0=150Ω.Calculate the value of the elements in the equivalent circuit for the output impedance.[R2=150Ω, L =811µH]10. An op-amp has the saturation voltages V+SAT= V+− 3VandV−SAT= V−+3 V, where V+=15 V and V−= −15 V. The current limited output current is IM= 30 mA. (a) Determinethe lowest load resistance that can be driven to full output without current limiting. (b)Determine the peak output voltage for a load resistance of 75 Ω.(c)Theop-ampisused1to realize a non-inverting amplifier with a gain of 5. The input waveform is a square wavewith a peak value of 1 V. Sketch the plot of the output voltage wave form for a capacitiveload of value CL=1µF. Assume that the op-amp does not slew. [400 Ω,2.25 V, slopes are±3 × 104V/s]11. The op-amp in the preceding problem has a slew rate of 0.75 V/µs. (a) Calculate the full-power bandwidth of the op-amp. (b) Calculate the peak value of the largest amplitudesine-wave that the op-amp can put out at frequency of 30 kHz if it is not to slew. (c)Calculate the largest peak-to-peak signal that the op-amp can put out at 30 kHz. Hint,assume that the amplitude of the input signal is increased until the output voltage waveformis fully converted into a triangle wave. [9.95 kHz, 6.25 V]12. A non-inverting amplifier with feedback resistors RFand R1has a resistor R2in serieswith its non-inverting input. The op-amp has the input bias current IB. Solve for the dccomponent of the output voltage due to IB. Assume that A0→∞, IOS=0,andVOS=0.[(1 + RF/R1) IB(R2− R1kRF)]13. A non-inverting op-amp with feedback resistors RF=100kΩ and R1=1kΩ has a dcoffset voltage of 1 V at its output when vI= 0. (a) If the input offset current and inputbias current can be neglected, calculate the input offset voltage VOS. (b) If the input offsetvoltage and input bias current can be neglected, calculate the input offset current IOS.(c)If the input offset voltage and input offset current can be neglected, calculate the input biascurrent IB. (d) The op-amp has the low-frequency open-loop gain A0=105. When eitherpower supply voltage is changed by 1 V, the dc offset at the op amp output changes by 0.5V. Calculate the power supply rejection ratio in µV/V. [9.9mV,20µA, 10 µA, 5 µV/V]14. A non-inverting amplifier has a resistor R1in series with the + input and feedback resistorsR2and RF. A series resistor R3and capacitor C are connected between the + and − inputs.Show that the effectiv e open-loop transfer function is given b yA0(s)=A (s)1+R3Cs1+(R1+ R2kRF+ R3) CsThus the R3− C network adds a pole-zero pair to the transfer function. Using a Bode plot,show how this can improve the stability of an amplifier when A (s) has more than one polebelow the unity-gain frequency.15. An op-amp has the low-frequency open-loop differential gain A0=105. The op amp is usedas a non-inverting amplifier with the feedback ratio vF/vO=0.0001. The gain with feedbackis found to be vO/vI= 9100. Calculate the common-mode rejection ratio