Instead of using a voltage-to-period converter, a constant phase LADAR system is configured using a voltage-to-frequency converter in which f o = K V V o , as shown in Figure P7.8. The distance to the...

Instead of using a voltage-to-period converter, a constant phase LADAR system is configured using a voltage-to-frequency converter in which f_o
= K_VV_o, as shown in Figure P7.8. The distance to the stationary, reflecting target is Lo meters. In the steady state, V_v
= 0 and V’ = V_set.

(A) Derive an expression for V_o
in the steady state.

(B) Now assume the target is receding at constant velocity v = L40. Assume steady state conditions so that V_v
= 0. Use the integrator transfer function to derive an expression for the steady state Vv. Note that V
_o
can be found by assuming L(t) and differentiating the Vo expression of part (A). Also note that V_v
and V_o
are both nonlinear functions of L.