sdr.LoopFilter

class sdr.LoopFilter

Implements a 2nd order, proportional-plus-integrator (PPI) loop filter.

Notes¶

Proportional-Plus-Integral Loop Filter Block Diagram¶

           +----+
       +-->| K1 |---------------------+
       |   +----+                     |
x[n] --+                              @--> y[n]
       |   +----+                     |
       +-->| K2 |-->@--------------+--+
           +----+   ^              |
                    |   +------+   |
                    +---| z^-1 |<--+
                        +------+

x[n] = Input signal
y[n] = Output signal
K1 = Proportional gain
K2 = Integral gain
z^-1 = Unit delay
@ = Adder

The transfer function of the loop filter is

H (z) = K_{1} + K_{2} \frac{1}{1 - z^{- 1}} = \frac{(K_{1} + K_{2}) - K_{1} z^{- 1}}{1 - z^{- 1}} .

The second-order proportional-plus-integrator loop filter can track a constant phase error and/or frequency error to zero. It cannot, however, track a constant chirp (frequency ramp) to zero.

References¶

Michael Rice, Digital Communications: A Discrete-Time Approach, Appendix C: Phase Locked Loops.

Examples¶

See the Phase-locked loops example.

Constructors¶

LoopFilter(noise_bandwidth: float, damping_factor: float, ...): Creates a 2nd order, proportional-plus-integrator (PPI) loop filter.

Special methods¶

__call__(x: ArrayLike) → NDArray: Filters the input signal $x [n]$ .

Methods¶

reset() → None: Resets the loop filter.

Properties¶

property noise_bandwidth : float: The normalized noise bandwidth $B_{n} T$ of the loop filter.

property damping_factor : float: The damping factor $ζ$ of the loop filter.

property proportional_gain : float: The proportional gain $K_{1}$ of the loop filter.

property integral_gain : float: The integral gain $K_{2}$ of the loop filter.

property iir : IIR: The underlying IIR filter used to implement the loop filter.