Question 4.65: Bipolar Power Supply Voltages The circuit in Figure P4-65 pr......
Bipolar Power Supply Voltages
The circuit in Figure P4-65 produces bipolar power supply voltages V_{POS} > 0 and V_{NEG} < 0 from a floating unipolar voltage source V_{REF} > 0. Note that the OP AMP output is grounded and that its +V_{CC} and ! V_{CC} terminals are connected to V_{POS} and V_{NEG}, respectively.
(a) Show that V_{POS} = +V_{NEG} ‘ 2 and V_{NEG} = ! V_{NEG} ‘ 2 even if the load resistors R_{POS} and R_{NEG} are not equal.
(b) If R_{POS} and R_{NEG} are not equal a current i_G must flow into or out of ground. How does the ungrounded voltage source V_{NEG} supply this ground current?
(c) In effect, the OP AMP creates a “virtual ground” at point A (V_A = 0) but draws no current in doing so. Why not just connect point A to a “real ground” and do away with the OP AMP?
(a) The OP AMP output is connected to ground and the negative input terminal, so v_N = 0 V. If the OP AMP is operating in its linear range, then v_N = v_P = 0 V, and the node between the two R resistors acts as a ground. The voltage V_{REF} appears across the two R resistors. Under the ideal OP AMP assumptions, no current enters the OP AMP through the positive terminal, so the current through the two R resistors must be i = V_{REF}/2R. The voltage drop across each R resistor is therefore V_{REF}/2. If the OP AMP causes the center node to have a voltage of 0 V, then the top node must be V_{POS} = V_{REF}/2 and the bottom node must be V_{NEG} = –V_{REF}/2. The load resistors have no influence on these voltages.
(b) The OP AMP is grounded and it will produce the required currents to satisfy the voltage conditions of the external circuit, as long as the OP AMP is operating in its linear region.
(c) Without the OP AMP, the load resistors R_{POS} and R_{NEG} would interact with the other resistors in the circuit and change the results. The OP AMP serves as a buffer to isolate the load and the reference voltage while still transferring the reference voltage to the output stage in a controlled manner.
Answer:
Presented above.