Autodyne Signal at Reflection Factor Value Modulation

An analysis of the autodyne effect of oscillators with linear frequency modulation

“…An analysis of the terms of delayed action, Г(t, τ) and δ(t, τ), made using their Taylor series expansion over delay time τ (similarly to that made in [10], where Ω D was replaced by Ω M ) showed that if the modulation period Т M = 2π/Ω M is by far larger than the delay time τ, then in Eq. (1) it is suffice to use the first terms in these expansions only.…”

“…where the numerical index near the square brackets denotes the order of approximation and p = ∆ω m (2ℓ/c) is the parameter of the autodyne signal distortion [10]. As we move from the reflecting target, the range ℓ in Eqs.…”

“…where τ 0 = R 0 C 0 , τ r = 2Q ld /ω n are the time constants of the auto-bias circuit and resonator, respectively, R 0 , C 0 are the resistance and capacitance of elements in the auto-bias circuit, ω n is the natural frequency of the resonator, α ij (i, j = 0,1), ε i (i = 0,1), β i,j (i, j = 0,1), ξ 1 are the differential parameters of the active oscillator element, which characterize the influence of small relative variations in the autodyne auto-bias а 0 = u 0 /U 0 , amplitude а 1 = а/А 0 and frequency χ = Δω/ω 0 of self-oscillations in the vicinity of stationary oscillations (discussed more extensively in [10]), u 0 = U -U 0 , а = А -А 0 , Δω = ω -ω 0 are the absolute autodyne variations in auto-bias U, amplitude А and frequency ω of oscillations with respect to the corresponding stationary values of U 0 , А 0 and ω 0 , В С = Г(t, τ)(2Q ld /Q ext )cosδ(t, τ); B S = Г(t, τ)(2Q ld /Q ext )sinδ(t, τ), Q l , Q ext are the loaded and external oscillator Q-factors, Г(t, τ) = Г[P(t, τ)/P(t)] 1/2 is the absolute value of the instantaneous reflectivity factor, P(t), P(t, τ) is the output autodyne power at the current point of time t and time (t -τ), respectively on the external oscillator load, Г is the coefficient of radiation damping in the course of its propagation to the target and back, δ(t, τ) = ψ(t) -ψ(t, τ) is the instantaneous wave phase difference between that in the current point of time ψ(t) and reflected radiation ψ(t, τ) back-reflected from the target within the time delay τ = 2ℓ/c, ℓ is the distance to the target, and c is the speed of radiowave propagation. Let us assume that the oscillator frequency varies with respect to the voltage applied to the varicap following the law…”

“…In order to solve the formulated problem in terms of a low-signal approximation from [10], let us write a system of linearized differential equations with a retarded argument for relative variations in bias a 0 , amplitude а 1 , and frequency χ of self-oscillations of a radio-pulse autodyne oscillator as follows:…”

Analysis of autodyne effect of an rf oscillator

“…The experimental investigation of the autodyne effect of an rf autodyne was performed in a measuring bench with an electromechanical imitator of a moving reflecting target described in [19,20]. As an autodyne oscillator we made use of a TIGEL-08 hybrid-integral module based on a double-mesa Gunn diode operating at the 8mm-wavelength [21].…”