Name: circuit gain and phase shift
Uploaded: 2024-07-08T13:20:02.000Z
Duration: 1 min 15 s
Channel: JoVE

Nei sistemi di comunicazione, il guadagno quantifica l'entità dell'amplificazione o dell'attenuazione del segnale.
Il guadagno di potenza denota il logaritmo comune del rapporto tra la potenza di uscita e la potenza di ingresso ed è espresso in bel.
Per le misurazioni pratiche, un decibel è comunemente usato. È una subunità equivalente a un decimo di bel.
Si consideri una rete con tensioni e resistenze di ingresso e uscita. Se la potenza di uscita è uguale alla potenza di ingresso in questa rete, il guadagno è di zero decibel.
Quando la potenza di uscita diventa il doppio della potenza di ingresso, il guadagno è di tre decibel. Al contrario, se la potenza di uscita scende alla metà della potenza di ingresso, il guadagno è di meno tre decibel.
In alternativa, la potenza può essere rappresentata utilizzando tensione e resistenza.
Le regole dei logaritmi vengono applicate per ottenere un'espressione per il guadagno di potenza in termini di rapporti di tensione e resistenza.
Quando la resistenza di ingresso è uguale alla resistenza di carico, il guadagno diventa proporzionale al rapporto di uscita e tensione di ingresso.
Allo stesso modo, il guadagno può essere rappresentato in termini di rapporti di corrente e resistenza.

risposta in frequenza

Guadagno e sfasamento sono proprietà dei circuiti lineari che descrivono l'effetto che un circuito ha su una tensione o corrente di ingresso sinusoidale. Il comportamento del circuito che contiene elementi reattivi dipenderà dalla frequenza della sinusoide di ingresso. Di conseguenza, si osserva che il guadagno e lo sfasamento saranno tutte funzioni di frequenza.


Guadagno:

Supponiamo che V_in sia l'ingresso e V_out sia il segnale di uscita su un circuito.

<img alt="Equation 1" src="/files/ftp_upload/15139/15139_Equation_1.svg" style="height: 20px;">
<img alt="Equation 2" src="/files/ftp_upload/15139/15139_Equation_2.svg" style="height: 16px;">


I segnali di ingresso e di uscita hanno rispettivamente l'ampiezza A e B e un angolo di fase di 0° e θ°.

Il guadagno del circuito dà la relazione tra le dimensioni delle sinusoidi di ingresso e di uscita. In particolare, il guadagno (K) è il rapporto tra l'ampiezza della sinusoide di uscita e l'ampiezza della sinusoide di ingresso.


<img alt="Equation 3" src="/files/ftp_upload/15139/15139_Equation_3.svg" style="height: 28px;">

Quando il guadagno K è maggiore dell'unità implica amplificazione, mentre un guadagno inferiore a uno indica attenuazione. Il guadagno è descritto utilizzando una scala logaritmica. Quando espresso in decibel (dB), il guadagno fornisce un modo conveniente per rappresentare numeri molto grandi e molto piccoli sulla stessa scala. Il guadagno in decibel si calcola utilizzando la formula:

<img alt="Equation 4" src="/files/ftp_upload/15139/15139_Equation_4.svg" style="height: 15px;">

Dove dB è il guadagno in decibel, K è il guadagno e log è il logaritmo in base 10.

Sfasamento:


Lo sfasamento si riferisce alla quantità di cui la fase del segnale di uscita viene ritardata o anticipata rispetto alla fase del segnale di ingresso. È la differenza angolare tra le sinusoidi di uscita e di ingresso. Il segnale di ingresso e di uscita ha un angolo di fase rispettivamente pari a 0° e θ°, quindi lo sfasamento (θ_shift) è dato da:

<img alt="Equation 5" src="/files/ftp_upload/15139/15139_Equation_5.svg" style="height: 18px;">


Uno spostamento θ positivo indica che il segnale di uscita è in ritardo rispetto al segnale di ingresso, mentre uno spostamento negativo significa che il segnale di uscita anticipa il segnale di ingresso.

Risposta in frequenza

Nei sistemi di comunicazione, il guadagno quantifica l'entità dell'amplificazione o dell'attenuazione del segnale.
Il guadagno di potenza denota il logaritmo comune del rapporto tra ...

Education

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JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

Frequency Response

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

Gain

circuit gain and phase shift

Circuit gain and phase shift describe how a linear circuit changes a sinusoidal input voltage or current. These properties matter in circuits with reactive elements, because the response depends on the input frequency. As the frequency changes, the gain and phase shift also change.

Gain compares the size of the output sinusoid to the size of the input sinusoid. If Vin is the input and Vout is the output, the gain K is the ratio of the output amplitude to the input amplitude. A gain greater than one means the circuit amplifies the signal, while a gain less than one means the circuit attenuates it.

Gain is often written on a logarithmic scale. When gain is expressed in decibels, or dB, it gives a practical way to show very large and very small values on the same scale. The dB value is found from the gain K using a base-10 logarithm.

Phase shift describes how much the output waveform is delayed or advanced compared with the input waveform. It is the angular difference between the input and output sinusoids. If the input has a phase angle of 0° and the output has a phase angle of θ°, then the phase shift is θ shift.

A positive phase shift means the output lags behind the input. A negative phase shift means the output leads the input. Together, gain and phase shift show both the size change and the timing change caused by a linear circuit.

Circuit Gain and Phase Shift

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gain

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Bode Plot Slope and Phase Changes

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key terms and concepts

Learn how linear circuits change sinusoidal signals through gain and phase shift, including amplitude ratio, decibels, and lag or lead.

Circuit Gain and Phase Shift | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Circuit Gain and Phase Shift

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