Here is a feedback system.

The closed loop transfer function for this system is given below.

• To see the derivation of this transfer function, click here.  Note that A(s) is the transfer function of the amplifier, i.e. A(s) = V_out(s)/[V₊(s) - V_-(s)]
• For the purposes of this problem:
• Assume that you are designing the amplifier
• Assume that Z₁and Z_f are equal resistors.
• Assume that the output stage of the amplifier has a corner frequency of 2 MHz.  This amplifier stage has been designed to provide adequate current output, etc., and the design is fixed.
• Assume that the DC gain of the amplifier needs to be 200,000.
• Every amplifier has at least one corner frequency.  (There are no infinite bandwidth amplifiers.)  Assume that you are responsible for the design of the input stage of the amplifier.  You need to specify the low frequency corner of the input stage of the amplifier so that the following specification holds.
• For the equal resistor case - outlined above - the system should have a phase margin of at least 45^o.