Chapter 11, Problem 1ST

E2.2 Consider a single-input neuron with a bias. We would like the output to be -1 for inputs less than 3 and +1 for inputs greater than or equal to 3. i. What kind of a transfer function is required? ii. What bias would you suggest? Is your bias in any way related to the input weight? If yes, how? iii. Summarize your network by naming the transfer function and stating the bias and the weight. Draw a diagram of the network.

E2.1 A single input neuron has a weight of 1.3 and a bias of 3.0. What possible kinds of transfer functions, from Table 2.1, could this neuron have, if its output is given below. In each case, give the value of the input that would produce these outputs. i. 1.6 ii. 1.0 iii. 0.9963 iv. -1.0

Q2. The slew rate of an amplifier can cause signal distortion at its output if wrongly chosen. State the criterion for selecting the slew rate of an amplifier to avoid signal distortion. A step signal of 5 mV is applied to an inverting amplifier shown in Figure 2, which has a slew rate of 0.05 V/us. Estimate the time required for the output voltage of the amplifier to reach within 10% of its final value. If the input to Figure 2 is a sinusoidal signal of 0.02 sin(2πft) V, determine the maximum frequency that can be applied to the circuit without causing signal distortion due to the limitation of its slew rate (0.05 V/µs). In order to minimise the output offset voltage of Figure 2, a compensating resistor should be added to Figure 2. Draw a modified circuit diagram that includes the compensating resistor. Determine the appropriate value for the compensating resistor. V₁ 2 ΚΩ 100 ΚΩ +

Q3) A single-phase semiconverter, shown in Fig.(3), is used to control the speed of small separately excited d.c. motor rated at 4.5 kW, 220V, 1500 rpm. The converter is connected to a single phase 230 V, 50 Hz supply. The armature resistance is Ra = 0.50 ohm and the armature circuit inductance is La 10 mH. The motor voltage constant is Ke D = 0.1 V/rpm. With the converter operates as a rectifier, the d.c. motor runs at 1200 rpm and carries an armature current of 16 A Assume that the motor current is continuous and ripple-free == (a) Draw and drive an equation for output voltage of semiconverter (b) The firing angle a. (c) The power delivered to the motor. (d) The supply power factor. R₂ FWD Thi Th₂ D. D FWD ep Fig.(3) Da ecte

Q3) A single-phase semiconverter, shown in Fig.(3), is used to control the speed of small separately excited d.c. motor rated at 4.5 kW, 220V, 1500 rpm. The converter is connected to a single phase 230 V, 50 Hz supply. The armature resistance is Ra = 0.50 ohm and the armature circuit inductance is La = 10 mH. The motor voltage constant is Ke Q=0.1 V/rpm. With the converter operates as a rectifier, the d.c. motor runs at 1200 rpm and carries an armature current of 16 A Assume that the motor current is continuous and ripple-free (a) Draw and drive an equation for output voltage of semiconverter (b) The firing angle a. (c) The power delivered to the motor. (d) The supply power factor. R FWD Th₁ Th₂ D. D FWD ep Fig.(3) Da ecte

E2.4 A two-layer neural network is to have four inputs and six outputs. The range of the outputs is to be continuous between 0 and 1. What can you tell about the network architecture? Specifically: i. How many neurons are required in each layer? ii. What are the dimensions of the first-layer and second-layer weight matrices? iii. What kinds of transfer functions can be used in each layer? iv. Are biases required in either layer?