Shown below is a circuit diagram of a frequency modulator. Vcc 1 7 Ro R1 LM 566 Co VCO 6. Message signal Vo 4 Um R2 LM566 is a voltage controlled oscillator (VCO) on a chip. The control voltage is to be applied to pin 5 and the FM output is the pin 4. According to the manufacturer's data sheet, the instantaneous frequency of the output signal (pin 4) and the control voltage vz (pin 5) are related by 2.4 f(t) [Vs - v5(t)] Hz, ROCOVS where Ro is in 2, Co is in F. It is required that 2 K2 < Ro < 20 KN. For those who are curious the data sheet is attached. Assume that the available power supply voltage is Vee = 10 V. For simplicity, assume that the amplitude of the FM output signal is 1 V. Also assume that the coupling capacitor connected to pin 5 is ideal (an open circuit for de and a short circuit for ac) and that the current drawn into pin 5 is negligibly small, so that the total voltage on pin 5 is v5(t) = (de level on pin 5 due to Voc) + Um (t). 1. Find an expression for the instantaneous angle of v,(t). 2. Find an expression for the FM signal v(t) in terms of the message signal vm(t) which is not necessarily a sinusoid. 3. You are required to design a frequency modulator using this circuit to meet the following requirements. Modulating signal (message) will have a bandwidth of 20 kHz and a voltage range of +25 mV Carrier frequency must be 1.2 MHz Bandwidth of the FM signal (as given by the Carson's rule) must be 160 kHz Find suitable values for the resistors Ro, R, and R2 and the capacitor Co-