To the conjunction sem que exists a corresponding preposition: sem. Therefore we can construct in Portuguese with an infinitive. The corresponding english preposition is without and we can construct in English with a gerund.
substitution of a subordinate clause introduced by sem que with an infinitivo
Foi aprovado sem que tivesse estudado.
Foi aprovado embora não teve estudado.*
Foi aprovado sem ter estudado.
He approvouved without having studied.
* Bit confusing. Embora is a concessive conjunction and refers to a simple factual connection. Purist say that the conjuntivo should be used and complain that the indicativo is used.
However there is no corresponding conjunction in English. If we want to construct with a conjunction, we have to reconstruct the english sentence.
sem que without (Without is a preposition. There is no corresponding conjunction in English.)
Ele deixou o local sem que o vissem.*
They didn' realise that he left the local.
Não saia** sem que eu permita.
You don't leave the house without my permission.
Esses ajustes podem ser realizados de antemão, sem que o aparelho tenha que ser montado.***
There is no need to have the machine installed in order to make adjustments.
Sabia todas as respostas sem que tivesse estudado.****
He knew all answers without having studied.
Vereador condenado por receber diárias sem que tivesse se ausentado do município..
A city council has been sentenced for having received a daily allowance without having left the town.
* Not realizing it and leaving happened at the same time. Therefore the imperfeito do conjuntivo it is to be used. It is a non reality.
** saia is an imperative
***The action described in the subordinate clause is imagined as accomplished in the present of the speaker and therefore the pretérito composto do conjuntivo is to be used. In conjuntivo the pretérito perfeito composto has almost the same function as the present perfect in English, see 12.2.3.
****The action, not learning, precedes the action in the past. Therefore the pretérito mais-que-perfeito composto do conjuntivo is to be used 12.2.4.