For low voltage signal or low power switching applications, optically isolated solid state relays (SSRs) with MOSFET outputs can provide several important advantages over traditional electromechanical relays (EMRs). A major challenge engineers face when using these relays is how to determine and find the maximum dynamic and static power that can be tolerated within the relay package. The operating frequency will basically impose the highest limit on the overall power consumption, so it is very important to accurately calculate the dynamic and static power consumption to ensure that the maximum power allowed by the solid state relay specifications is not exceeded. Finally, we will also provide application examples where solid state relays can gain advantages in terminal applications.
2.0 The dynamic power consumption of solid state relays is calculated
within the switching cycle time Tsw. Even if it is assumed that the drain-to-source voltage v(t) and drain current i(t) are linear at a certain moment, this linear conversion change is still an approximation, but it can meet practical applications.
The power consumption at a certain moment in the switching cycle can be expressed by the following equation:
p(t)sw = v(t) ● i(t) -------------------- Equation (1)
If the linear approximation is used, it can be seen from the above figure that v(t) and i(t) can be assumed to be linear functions of time, so: p(
t)sw = [ Vd (Tsw – t) / Tsw ] ● [ (Id ) (t) / Tsw ] ------------- Equation (2)
In the above equation, we assume that t=0 at the beginning of the switching cycle. The above graph shows that the switching time length at frequency f is Tp.
Simplifying equation (2), we can obtain:
p(t)sw = [{ (Vd) (Id) (Tsw-t) (t) }/ Tsw2 ] --------------------- Equation (3)
can be used to calculate the average power consumption within the switching time period Tsw:
t=Tsw
P(Tsw) = (1/ Tsw ) t="0" ∫ v(t) ● i(t) dt --------- Equation (4)
Integrating equation (3) and equation (4):
t = Tsw
P(Tsw) = (Vd) (Id) / Tsw3 ● t="0" ∫ ( Tsw-t) t dt
Solving the above integral, we can obtain the average power consumption within the switching period Tsw:
P(Tsw) = [ (Vd ) (Id) / 6 ] ------------------------ Equation (5)
Now we can calculate the total average power dissipation over the time period Tp. Note that Tsw(1) is the falling transition time t(f) of the SSR output voltage, and Tsw(2) is the rising transition time t(r) of the SSR output voltage:
P (Total Average over Tp) = [ (Vd) (Id) / 6] Tsw(1) / Tp + [ (Vd) (Id) /6 ] Tsw(2) / Tp + [ (Ron) (Id) 2] t(On-state)] / Tp + [ (Vd) (Ioff) t(off-state) ] / Tp --------- Equation (6)
Since f=1/Tp, the above equation can be expressed in terms of frequency and Tsw(1) is replaced by the falling transition time t(f) of the SSR output, and Tsw(2) is replaced by the rising transition time t(r) of the SSR output:
P(Total Average over Tp) = [ (Vd) (Id) / 6] t(f) (f) + [ (Vd) (Id) /6] t(r) (f) + [(Ron) (Id) 2 t(on-state) (f) + [ (Vd) (Ioff) t(off-state) (f) -------- Equation (7)
Please note that the above equation (6) shows that if Tsw is small relative to the time period Tp, the power consumption during the switching time is relatively small. We will discuss this in the following example. The above equation (7) also shows that as the frequency increases, the power consumption part of the switching cycle time Tsw will also increase, and bring about the limitation of the operating frequency.
Input power consumption:
The average power consumption in the time period TP is:
P(input) = [(Vf ● If ) t(on state)] / Tp -------- Equation (8)
or expressed in frequency:
P(input) = [(Vf ● If ) t(on state] ( f ) -------- Equation (9)
3.0 Practical Example of Calculating Power Dissipation
An ASSR-1510 solid-state relay is used to control the switching of a 1A load at 60V Vd, with a switching frequency of 100Hz, a duty cycle of 50%, and an input drive current of 5mA to the SSR.
(a) Calculate the output power dissipation, input power dissipation, and overall package power dissipation.
From the ASSR-1510 datasheet we can get:
Vf (max) = 1.7V
Frequency (f ) = 100 Hz,
on-resistance R(ON) = 0.5 Ω
t(f) = Output voltage falling transition time = 200 usec (estimated value, not specified in the datasheet)
t(r) = Output voltage rising transition time = 2 usec (estimated value, not specified in the datasheet)
Time period Tp = 1/f = 10 msec
50% duty cycle means t(On state) = 5 msec
t(off state) = 5 msec
From equation (7):
P(Total Average over Tp) = [ (Vd) (Id) / 6] t(f) (f) + [ (Vd) (Id) /6] t(r) (f) + [(Ron) (Id)2 t(on-state) (f) + [ (Vd) (Ioff) 50 mW t(off-state) (f) = 60V x 1 uA x 5 msec x 100 Hz = 300 mW t(off-state) (
f
) = 0.5Ω x (1A)2 x 5 msec x 100 Hz = 250 mW t(off-state) (f)
= 60V x 1 uA x 5 msec x 100 Hz = 300 mW t(
off-state) (f) = 0.5Ω x (1A)2 x 5 msec x 100 Hz = 250 mW t(off-state) (f) = 60V x 1 uA x 5 msec x 100 Hz = 300 mW
t(off-state) (f) = 60V x 1 uA x 5 msec x 100 Hz = 300 mW µW
Adding the above numbers together, we get an overall output power dissipation of 452mW.
The input power dissipation can be calculated using equation (9):
P(input) = [(Vf ● If ) t(on state] ( f ) = 1.7 x 5 mA x 5 msec x 100 Hz = 4.25 mW
Therefore, the overall average package power dissipation during the switching cycle is:
4.25 mW + 452 mW = 456.25 mW
This power dissipation is below the 540mW absolute maximum allowed by the ASSR-1510, so no power derating is required under this operating condition.
4.0 FET DRIVE CIRCUIT AND SOLID STATE RELAY FUNCTIONAL BLOCK DIAGRAM
The FET drive circuit in the SSR is powered by a photovoltaic power supply. The LED light flow received by the FET drive circuit is the only energy source for the FET drive circuit to drive the output MOSFET. The photovoltaic voltage is generated by 12 stacked photodiodes. Each photodiode can generate a voltage of about 0.5V, so the total voltage generated is 0.5x12=6V (typical value).
The magnitude of the generated photocurrent is the maximum current value used to charge the overall gate capacitance of the output MOSFET. The larger the photocurrent, the faster the gate voltage is charged to the photovoltaic voltage of the photodiode stack. Usually, the photocurrent generated by the stack voltage is about 20uA when the LED drive current is 10mA. A
fast turn-off circuit is used in the design of the FET drive circuit. The purpose of this circuit is to discharge the gate capacitance immediately when the LED current drops to zero and the SSR is turned off. This circuit is only briefly turned on when the photovoltaic voltage drops, and then the fast turn-off circuit can ensure that the SSR's turn-off time is much shorter than the SSR's turn-on time. , the power consumption of the FET drive circuit can be ignored, because the photocurrent generated is only about 20uA when the drive current is 10mA, and the stack voltage generated is about 6V.
Avago Technologies' FET drive circuit design also incorporates an output transient rejection circuit to ensure the ultra-high dVo/dt parameters and handling capabilities in the data sheet. The working principle of this circuit is that when the SSR is in the off state, any instantaneous high voltage change on the SSR contact will be coupled to the base of the transient rejection transistor through the capacitor and temporarily turned on, causing the gate to discharge to ensure that the output MOSFET will not turn on when the SSR output contact receives this transient high voltage pulse.
5.0 SSR Application Examples
(a) Typical Applications of SSRs
Fire Alarm Systems
Lighting Control
Instrumentation Systems
Dispensing Machines
Vending Machines
Test and Measurement
Traffic Control
Temperature Control
Security Systems
Medical Equipment
Elevator Control
Manufacturing Equipment
Commercial Washing Machines
Office and Business Machines
Navigation Systems
Defense and Military Hardware
(b) Solar Arrays Battery Charging
* The isolation diode can prevent the battery from discharging into the solar array due to parasitic resistance or leakage current when the SSR is turned off.
(c) Pulse telephone dialing
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