Understanding a PLL: Determine H(s) from Transfer Functions

anon6912 · Sep 25, 2017

I'm trying to implement a basic PLL. The diagram is given as follows:

Block diagram of a phase-locked loop with a summing junction, input Θ(s) with a plus sign and feedback Θ̂(s) with a minus sign, then blocks E_m, loop filter K_f(s), and VCO 1/S, output Θ̂(s), feedback path returning to the junction.

Where the transfer functions are given as follows:

Two transfer function equations: H_e(s) = Θ̂(s)/Θ(s) = K_f(s)E_m / (s + K_f(s)E_m) and H_δ(s) = Δ(s)/Θ(s) = s / (s + K_f(s)E_m).

To implement the PLL I need it to be as follows:

Block diagram of a PLL: three-phase voltages vsa, vsb, vsc enter an abc-to-dq transform block, which outputs vsd and vsq; vsq feeds block H(s), giving u_s, then an integrator producing the estimated angle θ_s, fed back to the transform.

How do I determine H(s) from the transfer functions that are given?

Thank you for your help

Baarken · Sep 25, 2017

Based on your 3rd picture, the block diagram reminds me of the so-called synchronous frame-PLL shown below (see attached pdf for more details). Here the loop filter is basically a PI regulator.

Se also "Operation of a phase locked loop system under distorted utility conditions" by V. Kaura and V. Blasko if you are interested in PLL under distorted inputs.

Block diagram of a synchronous reference frame phase-locked loop: a PI block in the forward path, a 1/s integrator producing theta, a 1/2pi block giving f, and abc to alpha-beta and dq-alpha-beta transforms feeding back.

Understanding a PLL: Determine H(s) from Transfer Functions

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