VNU JOURNAL O F SCIENCE. Mathem atics - Physics. T .xx. NC3AP, 2004
C H A R A C T E R I S T I C S O F P A R A M E T R I C A M P L I F I C A T I O N O F L O W - F R E Q U E N C Y R E G I O N S
M ai T h i H a T h a n h , N g u y e n V u C a m B in h , D a n g H u n g , D a n g T h i T h a n h T h u y , V u A nh P h i D epartm ent o f Physics, College o f Science, VN U
Abstract: We have carried out experiments ab ou t parametric amplification ca p a city at re g io n s h a vin g low pu m p in g fre q u e n c y an d c h a ra c te ris tic s o f th ese reg io ns. F ro m then s h o w e d th at p a ra m e tric am p lifica tion c o u ld b e d e te rm in e d at po ints c o rre s p on d in g to m a xim u m an d m in im u m vo lta g e -p u m p in g a m p litu d e s of p a ra m e tric re so n a n ce re g io n s o f so m e diffe re n t po ints. T h e s e n e w a m p lifica tio n reg io ns c o u ld h a ve p ra ctica l ap p lica tio n s, e sp ecia lly in c a s e o f u sin g low fre q u e n c y p u m p in g source.
As known th a t using a secondary resonance circuit (the contour I), w hich has the low resonance frequency fi0, can excited high-level param etric regions corresponding to roots am ong th e ones of differential equation which contains tim e-varying p aram etric (M athieu’s equations, N = 1, 3, 5, 7, 9), [1,2]. In these cases (except the case of N = 1), th e pum ping frequency fb is lower th a n th e resonance one (fb < f20 = ft|,) an d also lower th a n th e signal frequency flh m any tim es. On the basis of experim ental p aram etric m odulus, we have carried o u t to m easure p aram etric gain a t the points neighboring self-exciting param etric regions having different frequencies.
T he experim ental circuit is shown in Fig. 2, [1]. The in p u t signal has sm all value to m ake c u rre n t source. Because the signal is non-directional (taken o u t from the sam e position. u " ul, or uoy, ) an d also due to the beat, th e gain is m easured by com paring the m axim um ou tp u t am plitude with pum ping and w ithout pum ping. A lthough this m easurem ent could be u n ab le to affirm th e accurate gain com pletely, it also showed the am plification c h a rac teristic of t.he param etric system .
Because ihe pum ping am plitude a t th e down-threshold of the p aram etric generating region ( U ^ ) is r a th e r high, so th ere are frequency m ultiplying regions appeared among param etric gen e ratin g regions. We had also checked to affirm th a t th ere is no param etric am plification a t th e thresholds of these frequency m ultiplying regions because non-linear effects of the v aracto rs create high-level harm onics. T hat is also one fe atu re to determ ine p aram etric exciting an d am plifying regions.
Recognizing th a t th e re is param etric am plification u n d e r th e dow n-threshold of the param etric g enerating regions N = 3, 5, 7, 9 corresponding to fb » (2/3)Ç;o, fb * (2/5)fọ0, f|, « (2/7)fao, fb * (2/9)£m„ (f,0 = 202 KHz, f2n = 694 KHz, E0 = ov, show n in Fig. 3, [1]), the gain u n d e r the dow n-threshold of all these regions h ad been m easured w hen bias voltage is zero (Eo = 0 V).
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1 2 8 M a i T h i H a T h a n h , N g u y e n V u C a m B in h ...
In case o f N = 3: th e pum ping frequency: fb = 463 KHz, th e pum ping am plitude:
u b = 0.7V, th e signal frequency: flh = 695.9 KHz, th e signal am plitude: U lh = 2.5 mV, the o u tp u t am plitude: u*ut - 47.5 mV (tak e n o u t th e contour II - Fig.2, [1]), th e param etric gain: K = 19,
N = 5: fb = 262 KHz, u b = - 4.7db, f(h = 655.04 KHz, U lh = 2.5 mV, u £ }t = 60 mV, K = 24.
N = 7, fb = 179 KHz, u b = 3.3db, flh = 626.26 KHz, U th = 2.5 mV, = 70 raV, K = 28, N = 9, fu = 137.2 KHz, Ub = 8.3db, fth = 617.37 KHz. U th = 2.5 mV, u ;,2u’ = 95 mV, K = 38.
B eside th e s e regions (as th e signal f[h changes), th ere are still som e neighboring regions hav in g effect of am plification. We nee d to stu d y these regions carefully.
To com pare h ad also m ea su red th e capacity of am plification o f the region N = 1 under its dow n-threshold:
fh = 404 KHz, u b = -18.4db, flh = 201 KHz, Uth = 4 mV, u ™ = 100 mV, K = 25.
W ith a tw o-contour p aram etric am plification system : fb as f10 + f20, f,h * £>0> having regeneration an d no frequency tran sform ation: fb = f10+ f20 = 896.2 KHz, U b = 1.7db, f,h(2) = 710 KHz. UIh<2) = 3.25 mV, = 67.5m V, K = 20.
U n d e r th e thresh o ld o f th e m odulated region located a t th e left of th e fifth region N = 5, th e m ea su red gain is:
fb = 256 KHz, u b = 9.8db, fth = 647.18 KHz, U lh = 1.5 mV, = 150 mV, K = 100.
F ig .l. Studying the parametric amplification of Fig.2. The amplification response K(fb) under the parametric regions N = 1 and N = 3 the down-threshold of the region N = 5 In low Q -factor sy stem s (Qt an d Q2 are ab out 40 -7- 50 or lower), if th e m ultiple- deviation coefficient n = f2(/f|(> > 3, Ị2], th e gain a t points neighboring th ese regions was m easured.
T he th ird g en e ratin g region, N = 3, is show n in th e F ig .l. R ealize t h a t two regions N = 1 và N = 3 a r e fa r aw ay ab out 15KHz.
C h a r a c te r is tic s o f p a r a m e tr i c a m p l i f ic a t io n of... 129
M easured th e gain K an d the Q -factor of th e region N = 1:
- U n d e r its down-threshold: fh = 721,6 KHz, U b = -12.9db (about 0.15V), fth = 366 KHz, u ,h = 20 mV, K = 8, Q = 328.
- Upper its up-threshold: fb = 690 KHz, U b =5db (about 1.35V), f0 = 365KHz, flh = 350KHz, u th = 2 mV, U Í2 = 32.5 mV, K = 16, Q = 328.
Also m easured th e gain K and the Q -factor o f th e region N = 3:
- U nder its down-threshold: fb = 751.9KHZ, Ub = l.ld b (a b o u t 0.75V), ftha: f2o=1120KHz, Ujh = 3 mV, K = 25, Q = 560.
- N eighboring th e up-threshold: fb =748.09K Hz, u b = 2db(about 0.85V), flh =1120KHz, U lh = 0.35 mV, K = 17.
- U p p e r th e up-threshold: f|, = 764.9 KHz, Ub = 8.4db (about 1.7V), fth = 1150 KHz, Ulh = 2 mV, K = 85, high-Q.
R ealize th a t there is p aram etric am plification n o t only u n d e r th e dow n-threshold of th e param etric gen e ratin g region N = 3 b u t also u p p e r th e u p -th re sh o ld a n d neighboring th is region. In such cases of th e ra th e r high p u m ping am p litu d e, it is necessary to d ete rm in e th e role of noise, from th en th e role of p a ra m e tric am p litu d e a t th ese points m ight be affirm ed clearly.
W ith th e fifth region N = 5, th e re is also p a ra m e tric am plification s im ila r to one of the region N = 3. Three curves K(fb) corresponding to d ifferent pu m p in g am p litu d es Ub(Ub <
U bN = 7.4db) a r e shown in the Pig. 2. W hen u b approach to UbN, th e gain increases (Q = 2423.7 - curve (1)), frequency band is n arrow (2Afb = 0.245 KHz).
A com m on phenom enon of th e s e param etric regions is alw ays to h a v e b ea ts w hen the K-factor is tu n ed to m axim um . The beat frequency could be able to appro ach to zero a s the case o f incoherent reception of single p aram etric am plification.
C o n c lu s io n s
* T he p aram etric am plification can be re alised a t v ario u s regions, n e a r N = 3, 5, 7 (under dow n-threshold , u p p e r up-theshold a n d neighboring regions).
* W hen K -factor is tu n e d to m axim um , i t alw ays h av e th e b ea ts (b e at frequencies could be to approach to zero comme incoherent case)
* It can be used som e low pum ping frequencies for h igh signal, if flh an d fb are tu ned correctly.
R e fe re n c e s
1. N. T. H. Hanh, N. V. c . Binh, Đ. T. Kien, V. A. Phi, A bout one experimental modulus having excited the parametric phenomena by low pum p in g frequency, Science Report, (2004) Departm ent of Physics, College of Science, VNU.
2. N. V. c . Binh, V. L. T. Ha, N. D. Lam, Đ. T. M. Nguyet, V. A. P hi, The influence o f multiple-deviation coefficient n to param etric generating regions N = 3, 5, 7, Science Report, (2004) D epartm ent of Physics, College of Science, VNU.
