Q10. Find component values to make the transfer function frequency independent

The filter given below has the transfer function T(s)= v_{out}(s)/v_{in}(s) where s is the Laplace variable. If C_1 \neq C_2, and R_1 \neq R_2, given C_1, R_1, find C_2, and  R_2, if gain is frequency independent and equal to -G where G is a real positive number. 

Q9. Find the resistance

The op-amp below is ideal except for having a finite open-loop gain A_0 and is used to realize an inverting amplifier whose gain has a nominal (desired) value G=-R_2/R_1. To compensate for the gain reduction due to the finite gain A_0, a resistance R_c is shunted across R_1. Find the value for R_c  which gives perfect compensation so that the setup gives gain G=-R_2/R_1. 

Q9. Find the output voltage

The differential gain of an op-amp is 4000 and the value of CMRR is 150. Find the output voltage of the op-amp if the non-inverting and inverting terminals have 200\mu\text{V} and 160\mu\text{V}, respectively. 

Q8. Find the largest input sine wave RMS value

An op-amp uses \pm15\text{V} supplies and operates linearly in the output range -14\text{V} to +14\text{V}. If used in an inverting amplifier configuration of gain -100, what is the rms value of the largest sine wave that can be applied at the input without clipping?

Q7. Find operating regions

Consider an op-amp with f_t =20\text{MHz}, SR=10 \text{V}/\mu\text{s}, and V_{omax}=10\text{V}. The op-amp is used to design of a non-inverting amplifier with a nominal gain, G of 10. For a sinusoidal input, V_p\text{sin}(2\pi f_{in}t+\theta) with peak amplitude V_p and frequency f_{in}, find 

Q6. Find the dc input bias cancelling resistor

Consider the analogue integrator below with explicitly shown V_{OS}=2\text{mV} input dc offset voltage at the non-inverting input; and  input bias currents I_B=0.1\mu\text{A} and input offset current  I_{OS}=20\text{nA} (which can be used to calculate I_{BI} and I_{BN} below). To provide a finite dc gain, a resistor R_2=1\text{M}\Omega is connected across the capacitor C_2=10\text{nF}. To compensate for the effect of I_B, a resistor R_3 is connected to the non-inverting input terminal. Find the value of R_3. Here, R_1=10\text{k}\Omega. 

Q5. Find the dc offset voltage at the output

Consider the difference amplifier below with explicitly shown V_{OS}=5\text{mV}  input dc offset voltage at the non-inverting input; and  input bias currents I_B=1\mu\text{A} and input offset current I_{OS}=0.2\mu\text{A} (which can be used to calculate I_{BI} and I_{BN} below). Find the dc offset voltage at the output. Here, R_1=R_3=10\text{k}\Omega, and R_2=R_4=1\text{M}\Omega.

Q4. Find the closed loop gain

Consider the integrator shown below with finite loop gain A_0 , and input resistance R_{in} as shown below. Find the closed loop gain v_{out}/v_{in}.